perf(query): use UNION of index seeks for ListUsers login equality (#12701)

<!-- CURSOR_AGENT_PR_BODY_BEGIN -->
# Which Problems Are Solved

Login V2 `ListUsers` lookups of the form username OR email (and email OR
phone) hash-join the full `users14` / `users14_humans` tables, then
filter. That cost grows with instance size (~40ms at 10k users, ~650ms
at 200k).

Top-level login-name equals already used an indexed join, but the same
login-name filter inside an `OrQuery` fell back to the slow view-based
exists query.

# How the Problems Are Solved

**TL;DR:** equality lookups on username, email, phone, or login name
become `INNER JOIN (UNION of indexed ID seeks) AS matches`. Mixed /
contains / name searches keep the old WHERE shape.

### Reviewer map

| Read first | Why |
| --- | --- |
| `internal/query/user_login_equality.go` | Typed filters + extractor +
UNION join |
| `internal/query/user.go` (`prepareUsersQuery`, constructors) | Wiring;
username/email/phone equals return `lowerEqualsFilter` |
| `cmd/setup/76.go` + `cmd/setup/76/*.sql` | Concurrent indexes for
existing deployments; drop invalid leftovers |
| `internal/query/projection/user.go` | Same indexes in `Init()` for new
databases |
| `internal/query/user_login_name_exists_test.go` | SQL-shape coverage |
| `internal/api/grpc/user/v2/integration_test/query_test.go` | Nested
username AND/OR user results |

### Query rewrite

- Extract one equals leaf, a flat `OrQuery` of those leaves, or the same
nested under `AndQuery`. Remaining AND conjuncts stay as WHERE. Equality
nested under `OrQuery` / `NotQuery` is left as WHERE.
- Login-name equals is a UNION arm that reuses `login_names3_users` SQL,
so it works inside OR as well as at the top level.
- EQUALS seeks use `LOWER(col)` for the index, then recheck `col =
value` so case-sensitive searches do not match extra rows.
EQUALS_IGNORE_CASE is unchanged.
- Empty OR arms are not skipped (that would change OR meaning); mixed
empty-OR falls back to WHERE. Login UI already omits empty arms.

### Indexes

- Setup 76: `CREATE INDEX CONCURRENTLY IF NOT EXISTS` on
`users14_username_lower_idx` `(instance_id, LOWER(username))` and
`users14_humans_phone_lower_idx` `(instance_id, LOWER(phone))`. Not
wrapped in a transaction.
- Before create, drop any leftover `pg_index.indisvalid = false` indexes
of those names (failed/cancelled `CREATE INDEX CONCURRENTLY`). `IF NOT
EXISTS` would otherwise skip rebuild.
- `Init()` creates the same indexes without `CONCURRENTLY` (empty
tables). Existing `users14_username` and email lower indexes are
unchanged.

# Additional Changes

- Unit tests assert UNION SQL for username OR email, email OR phone,
login name OR email, username OR username, nested `AndQuery(loginName,
org)`, and nested `AndQuery(Or(...), org)`; that contains / display-name
/ mixed OR / nested `OrQuery(AndQuery(...), ...)` do not UNION; that
email EQUALS rechecks the raw column; and that empty-OR is not
extracted.
- Setup 76 sqlmock coverage: missing `users14` skips work; valid/absent
indexes only create; invalid leftover username index is dropped then
both creates run.
- `TestServer_ListUsers_UsernameAndOr` checks live results: org AND
(alice OR bob) returns both users, sibling username AND is empty, nested
`AndQuery(Or(...), org)` returns both.

# Additional Context

- Base branch: `main`
- Extends the login-name equals rewrite from #12460 to
username/email/phone OR trees used by Login V2 search.

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---------

Co-authored-by: Cursor Agent <[email protected]>
Co-authored-by: Silvan <[email protected]>

internal/api/grpc/user/v2/integration_test/query_test.go

@@ -1252,6 +1252,64 @@ func TestServer_SystemUsers_ListUsers(t *testing.T) {
 	}
 }
 
+func TestServer_ListUsers_UsernameAndOr(t *testing.T) {
+	iamOwnerCtx := InstancePermissionV2.WithAuthorizationToken(OrgCTX, integration.UserTypeIAMOwner)
+	orgResp := InstancePermissionV2.CreateOrganization(iamOwnerCtx, integration.OrganizationName(), integration.Email())
+	alice := createUser(iamOwnerCtx, InstancePermissionV2, orgResp.OrganizationId, false)
+	bob := createUser(iamOwnerCtx, InstancePermissionV2, orgResp.OrganizationId, false)
+	orgQuery := OrganizationIdQuery(orgResp.OrganizationId)
+
+	tests := []struct {
+		name          string
+		queries       []*user.SearchQuery
+		wantUsernames []string
+	}{
+		{
+			name: "org and username or username",
+			queries: []*user.SearchQuery{
+				orgQuery,
+				OrQuery([]*user.SearchQuery{UsernameQuery(alice.Username), UsernameQuery(bob.Username)}),
+			},
+			wantUsernames: []string{alice.Username, bob.Username},
+		},
+		{
+			name: "org and sibling usernames",
+			queries: []*user.SearchQuery{
+				orgQuery,
+				UsernameQuery(alice.Username),
+				UsernameQuery(bob.Username),
+			},
+		},
+		{
+			name: "nested and of or and org",
+			queries: []*user.SearchQuery{
+				AndQuery([]*user.SearchQuery{
+					OrQuery([]*user.SearchQuery{UsernameQuery(alice.Username), UsernameQuery(bob.Username)}),
+					orgQuery,
+				}),
+			},
+			wantUsernames: []string{alice.Username, bob.Username},
+		},
+	}
+
+	for _, tt := range tests {
+		t.Run(tt.name, func(t *testing.T) {
+			req := &user.ListUsersRequest{Queries: tt.queries}
+			retryDuration, tick := integration.WaitForAndTickWithMaxDuration(iamOwnerCtx, 20*time.Second)
+			require.EventuallyWithT(t, func(ttt *assert.CollectT) {
+				got, err := InstancePermissionV2.Client.UserV2.ListUsers(iamOwnerCtx, req)
+				require.NoError(ttt, err)
+
+				gotUsernames := make([]string, 0, len(got.GetResult()))
+				for _, u := range got.GetResult() {
+					gotUsernames = append(gotUsernames, u.GetUsername())
+				}
+				assert.ElementsMatch(ttt, tt.wantUsernames, gotUsernames)
+			}, retryDuration, tick, "timeout waiting for expected user result")
+		})
+	}
+}
+
 func InUserIDsQuery(ids []string) *user.SearchQuery {
 	return &user.SearchQuery{
 		Query: &user.SearchQuery_InUserIdsQuery{
@@ -1312,6 +1370,16 @@ func OrQuery(queries []*user.SearchQuery) *user.SearchQuery {
 	}
 }
 
+func AndQuery(queries []*user.SearchQuery) *user.SearchQuery {
+	return &user.SearchQuery{
+		Query: &user.SearchQuery_AndQuery{
+			AndQuery: &user.AndQuery{
+				Queries: queries,
+			},
+		},
+	}
+}
+
 func MetadataKeyContainsQuery(metadataKey string) *user.SearchQuery {
 	return &user.SearchQuery{
 		Query: &user.SearchQuery_MetadataKeyFilter{

internal/query/projection/user.go

@@ -101,6 +101,7 @@ func (*userProjection) Init() *old_handler.Check {
 		},
 			handler.NewPrimaryKey(UserInstanceIDCol, UserIDCol),
 			handler.WithIndex(handler.NewIndex("username", []string{UserUsernameCol})),
+			handler.WithIndex(handler.NewIndex("username_lower", []string{UserInstanceIDCol, "LOWER(" + UserUsernameCol + ")"})),
 			handler.WithIndex(handler.NewIndex("resource_owner", []string{UserResourceOwnerCol})),
 		),
 		handler.NewSuffixedTable([]*handler.InitColumn{
@@ -125,6 +126,7 @@ func (*userProjection) Init() *old_handler.Check {
 			UserHumanSuffix,
 			handler.WithForeignKey(handler.NewForeignKeyOfPublicKeys()),
 			handler.WithIndex(handler.NewIndex("email", []string{HumanUserInstanceIDCol, "LOWER(" + HumanEmailCol + ")"})),
+			handler.WithIndex(handler.NewIndex("phone_lower", []string{HumanUserInstanceIDCol, "LOWER(" + HumanPhoneCol + ")"})),
 		),
 		handler.NewSuffixedTable([]*handler.InitColumn{
 			handler.NewColumn(MachineUserIDCol, handler.ColumnTypeText),

internal/query/user.go

@@ -747,7 +747,7 @@ func NewUserResourceOwnerSearchQuery(value string, comparison TextComparison) (S
 }
 
 func NewUserUsernameSearchQuery(value string, comparison TextComparison) (SearchQuery, error) {
-	return NewTextQuery(UserUsernameCol, value, comparison)
+	return newLowerEqualsSearchQuery(UserUsernameCol, userTable, UserIDCol, value, comparison)
 }
 
 func NewUserFirstNameSearchQuery(value string, comparison TextComparison) (SearchQuery, error) {
@@ -767,11 +767,11 @@ func NewUserDisplayNameSearchQuery(value string, comparison TextComparison) (Sea
 }
 
 func NewUserEmailSearchQuery(value string, comparison TextComparison) (SearchQuery, error) {
-	return NewTextQuery(HumanEmailCol, value, comparison)
+	return newLowerEqualsSearchQuery(HumanEmailCol, humanTable, HumanUserIDCol, value, comparison)
 }
 
 func NewUserPhoneSearchQuery(value string, comparison TextComparison) (SearchQuery, error) {
-	return NewTextQuery(HumanPhoneCol, value, comparison)
+	return newLowerEqualsSearchQuery(HumanPhoneCol, humanTable, HumanUserIDCol, value, comparison)
 }
 
 func NewUserVerifiedEmailSearchQuery(value string) (SearchQuery, error) {
@@ -801,8 +801,8 @@ var userLoginNameMatchesQuery string
 var userLoginNameMatchesCaseSensitiveQuery string
 
 // NewUserLoginNameExistsQuery filters users by login name.
-// Equals / EqualsIgnoreCase use a planner marker rewritten in prepareUsersQuery
-// into an indexed join on login_names3_users. Other comparisons use the view.
+// Equals / EqualsIgnoreCase are rewritten in prepareUsersQuery into an indexed
+// ID-seek. Other comparisons use the login_names3 view.
 func NewUserLoginNameExistsQuery(value string, comparison TextComparison) (SearchQuery, error) {
 	if comparison == TextEquals || comparison == TextEqualsIgnoreCase {
 		return newLoginNameEqualsFilter(value, comparison == TextEqualsIgnoreCase)
@@ -842,126 +842,6 @@ func newLoginNameExistsViewQuery(value string, comparison TextComparison) (Searc
 	)
 }
 
-// loginNameEqualsFilter marks a login-name equality filter for prepareUsersQuery
-// to rewrite as an indexed join. Unextracted markers (e.g. inside OrQuery) fall
-// back to the view-based exists query.
-type loginNameEqualsFilter struct {
-	username   string
-	domain     string
-	loginName  string
-	ignoreCase bool
-}
-
-func newLoginNameEqualsFilter(value string, ignoreCase bool) (*loginNameEqualsFilter, error) {
-	if ignoreCase {
-		value = strings.ToLower(value)
-	}
-	username := value
-	domainIndex := strings.LastIndex(value, "@")
-	var domainSuffix string
-	// split between the last @ (so ignore it if the login name ends with it)
-	if domainIndex > 0 && domainIndex != len(value)-1 {
-		domainSuffix = value[domainIndex+1:]
-		username = value[:domainIndex]
-	}
-	return &loginNameEqualsFilter{
-		username:   username,
-		domain:     domainSuffix,
-		loginName:  value,
-		ignoreCase: ignoreCase,
-	}, nil
-}
-
-func (q *loginNameEqualsFilter) comparison() TextComparison {
-	if q.ignoreCase {
-		return TextEqualsIgnoreCase
-	}
-	return TextEquals
-}
-
-func (q *loginNameEqualsFilter) fallback() SearchQuery {
-	// Equals / EqualsIgnoreCase construction cannot fail for valid columns.
-	fallback, _ := newLoginNameExistsViewQuery(q.loginName, q.comparison())
-	return fallback
-}
-
-func (q *loginNameEqualsFilter) toQuery(query sq.SelectBuilder) sq.SelectBuilder {
-	return q.fallback().toQuery(query)
-}
-
-func (q *loginNameEqualsFilter) Col() Column {
-	return UserIDCol
-}
-
-func (q *loginNameEqualsFilter) comp() sq.Sqlizer {
-	return q.fallback().comp()
-}
-
-func (q *loginNameEqualsFilter) matchesArgs(instanceID string) []interface{} {
-	return []interface{}{
-		instanceID,
-		instanceID,
-		q.domain,
-		instanceID,
-		q.username,
-		q.loginName,
-		q.username,
-		q.domain,
-		q.loginName,
-	}
-}
-
-func (q *loginNameEqualsFilter) joinMatches(instanceID string) sq.Sqlizer {
-	subQuery := userLoginNameMatchesQuery
-	if !q.ignoreCase {
-		subQuery = userLoginNameMatchesCaseSensitiveQuery
-	}
-	return sq.Expr(
-		"INNER JOIN ("+subQuery+") AS login_name_matches ON "+UserIDCol.identifier()+" = login_name_matches.user_id",
-		q.matchesArgs(instanceID)...,
-	)
-}
-
-// extractLoginNameEqualsFilter extracts one login-name equals marker from
-// top-level or AndQuery filters. Markers inside OrQuery / NotQuery are kept.
-func extractLoginNameEqualsFilter(queries []SearchQuery) (filter *loginNameEqualsFilter, remaining []SearchQuery, ok bool) {
-	remaining = make([]SearchQuery, 0, len(queries))
-	var found *loginNameEqualsFilter
-
-	for _, qry := range queries {
-		switch v := qry.(type) {
-		case *loginNameEqualsFilter:
-			if found != nil {
-				return nil, queries, false
-			}
-			found = v
-		case *AndQuery:
-			inner, rest, extracted := extractLoginNameEqualsFilter(v.queries)
-			if !extracted {
-				remaining = append(remaining, qry)
-				continue
-			}
-			if found != nil {
-				return nil, queries, false
-			}
-			found = inner
-			if len(rest) == 1 {
-				remaining = append(remaining, rest[0])
-			} else if len(rest) > 1 {
-				andQuery, _ := NewAndQuery(rest...)
-				remaining = append(remaining, andQuery)
-			}
-		default:
-			remaining = append(remaining, qry)
-		}
-	}
-
-	if found == nil {
-		return nil, queries, false
-	}
-	return found, remaining, true
-}
-
 func (q *UserSearchQueries) hasMetadataFilter() bool {
 	return searchQueriesHaveMetadataFilter(q.Queries)
 }
@@ -1416,18 +1296,15 @@ func prepareUserUniqueQuery() (sq.SelectBuilder, func(*sql.Row) (bool, error)) {
 // It is not possible to pass more filters to the returned query, as they need to be applied in the sub-select.
 //
 // Metadata JOIN and DISTINCT are only applied when a metadata filter is present.
-// Login-name equals markers are rewritten into an indexed join when extractable.
+// Login-equality filters (username, email, phone, login name EQUALS /
+// EQUALS_IGNORE_CASE) become an indexed UNION of ID seeks.
 func (q *UserSearchQueries) prepareUsersQuery(ctx context.Context, permissionCheckV2 bool) (sq.SelectBuilder, func(*sql.Rows) (*Users, error)) {
 	if q.SortingColumn.isZero() {
 		q.SortingColumn = UserIDCol
 	}
 
 	instanceID := authz.GetInstance(ctx).InstanceID()
-	loginNameFilter, remainingFilters, loginNameExtracted := extractLoginNameEqualsFilter(q.Queries)
-	filters := q.Queries
-	if loginNameExtracted {
-		filters = remainingFilters
-	}
+	loginEqualitySeeks, filters, loginEqualityExtracted := extractLoginEqualitySeeks(instanceID, q.Queries)
 	needsMetadataJoin := q.hasMetadataFilter()
 
 	// start building the sub-select
@@ -1469,8 +1346,8 @@ func (q *UserSearchQueries) prepareUsersQuery(ctx context.Context, permissionChe
 		JoinClause(joinLoginNames).
 		Where(sq.Eq{UserInstanceIDCol.identifier(): instanceID})
 
-	if loginNameExtracted {
-		query = query.JoinClause(loginNameFilter.joinMatches(instanceID))
+	if loginEqualityExtracted {
+		query = query.JoinClause(joinLoginEqualitySeeks(loginEqualitySeeks))
 	}
 
 	if needsMetadataJoin {

internal/query/user_login_equality.go

@@ -0,0 +1,227 @@
+package query
+
+import (
+	"strings"
+
+	sq "github.com/Masterminds/squirrel"
+)
+
+type loginEqualitySeek struct {
+	sql  string
+	args []interface{}
+}
+
+// loginNameEqualsFilter marks login-name equality for an indexed ID-seek in
+// prepareUsersQuery. Unextracted markers fall back to the view-based exists query.
+type loginNameEqualsFilter struct {
+	username   string
+	domain     string
+	loginName  string
+	ignoreCase bool
+}
+
+func newLoginNameEqualsFilter(value string, ignoreCase bool) (*loginNameEqualsFilter, error) {
+	if ignoreCase {
+		value = strings.ToLower(value)
+	}
+	username := value
+	domainIndex := strings.LastIndex(value, "@")
+	var domainSuffix string
+	// split between the last @ (so ignore it if the login name ends with it)
+	if domainIndex > 0 && domainIndex != len(value)-1 {
+		domainSuffix = value[domainIndex+1:]
+		username = value[:domainIndex]
+	}
+	return &loginNameEqualsFilter{
+		username:   username,
+		domain:     domainSuffix,
+		loginName:  value,
+		ignoreCase: ignoreCase,
+	}, nil
+}
+
+func (q *loginNameEqualsFilter) comparison() TextComparison {
+	if q.ignoreCase {
+		return TextEqualsIgnoreCase
+	}
+	return TextEquals
+}
+
+func (q *loginNameEqualsFilter) fallback() SearchQuery {
+	fallback, _ := newLoginNameExistsViewQuery(q.loginName, q.comparison())
+	return fallback
+}
+
+func (q *loginNameEqualsFilter) toQuery(query sq.SelectBuilder) sq.SelectBuilder {
+	return q.fallback().toQuery(query)
+}
+
+func (q *loginNameEqualsFilter) Col() Column {
+	return UserIDCol
+}
+
+func (q *loginNameEqualsFilter) comp() sq.Sqlizer {
+	return q.fallback().comp()
+}
+
+func (q *loginNameEqualsFilter) matchesArgs(instanceID string) []interface{} {
+	return []interface{}{
+		instanceID,
+		instanceID,
+		q.domain,
+		instanceID,
+		q.username,
+		q.loginName,
+		q.username,
+		q.domain,
+		q.loginName,
+	}
+}
+
+func (q *loginNameEqualsFilter) idSeek(instanceID string) loginEqualitySeek {
+	// userLoginNameMatchesQuery uses *_lower columns; the _case_sensitive embed uses raw columns.
+	subQuery := userLoginNameMatchesQuery
+	if !q.ignoreCase {
+		subQuery = userLoginNameMatchesCaseSensitiveQuery
+	}
+	return loginEqualitySeek{
+		sql:  "SELECT user_id AS id FROM (" + subQuery + ") AS login_name_matches",
+		args: q.matchesArgs(instanceID),
+	}
+}
+
+// lowerEqualsFilter is username, email, or phone EQUALS / EQUALS_IGNORE_CASE.
+// Unextracted filters compile to the same WHERE clause as textQuery.
+type lowerEqualsFilter struct {
+	textQuery
+	tbl   table
+	idCol Column
+}
+
+func newLowerEqualsSearchQuery(valueCol Column, tbl table, idCol Column, value string, comparison TextComparison) (SearchQuery, error) {
+	if comparison != TextEquals && comparison != TextEqualsIgnoreCase {
+		return NewTextQuery(valueCol, value, comparison)
+	}
+	tq, err := NewTextQuery(valueCol, value, comparison)
+	if err != nil {
+		return nil, err
+	}
+	return &lowerEqualsFilter{textQuery: *tq, tbl: tbl, idCol: idCol}, nil
+}
+
+func (q *lowerEqualsFilter) idSeek(instanceID string) loginEqualitySeek {
+	sql := "SELECT " + q.idCol.identifier() + " AS id FROM " + q.tbl.identifier() +
+		" WHERE " + q.tbl.InstanceIDIdentifier() + " = ? AND LOWER(" + q.Column.identifier() + ") = "
+	args := []interface{}{instanceID}
+	if q.Compare == TextEquals {
+		sql += "LOWER(?) AND " + q.Column.identifier() + " = ?"
+		args = append(args, q.Text, q.Text)
+	} else {
+		sql += "?"
+		args = append(args, strings.ToLower(q.Text))
+	}
+	return loginEqualitySeek{sql: sql, args: args}
+}
+
+func loginEqualitySeekFromLeaf(instanceID string, qry SearchQuery) (loginEqualitySeek, bool) {
+	switch v := qry.(type) {
+	case *loginNameEqualsFilter:
+		if v.loginName == "" {
+			return loginEqualitySeek{}, false
+		}
+		return v.idSeek(instanceID), true
+	case *lowerEqualsFilter:
+		if v.Text == "" {
+			return loginEqualitySeek{}, false
+		}
+		return v.idSeek(instanceID), true
+	default:
+		return loginEqualitySeek{}, false
+	}
+}
+
+func loginEqualitySeeksFromQuery(instanceID string, qry SearchQuery) ([]loginEqualitySeek, bool) {
+	if seek, ok := loginEqualitySeekFromLeaf(instanceID, qry); ok {
+		return []loginEqualitySeek{seek}, true
+	}
+	or, ok := qry.(*OrQuery)
+	if !ok {
+		return nil, false
+	}
+	seeks := make([]loginEqualitySeek, 0, len(or.queries))
+	for _, inner := range or.queries {
+		seek, ok := loginEqualitySeekFromLeaf(instanceID, inner)
+		if !ok {
+			return nil, false
+		}
+		seeks = append(seeks, seek)
+	}
+	if len(seeks) == 0 {
+		return nil, false
+	}
+	return seeks, true
+}
+
+// extractLoginEqualitySeeks pulls one login-equality filter from queries.
+// A match may be a top-level equals leaf, a flat OrQuery of those leaves, or
+// the same nested under AndQuery. Remaining AND conjuncts stay as WHERE.
+// Equality nested under OrQuery or NotQuery is not extracted.
+func extractLoginEqualitySeeks(instanceID string, queries []SearchQuery) ([]loginEqualitySeek, []SearchQuery, bool) {
+	for i, qry := range queries {
+		if and, ok := qry.(*AndQuery); ok {
+			seeks, andRest, ok := extractLoginEqualitySeeks(instanceID, and.queries)
+			if !ok {
+				continue
+			}
+			return seeks, spliceRemainingQuery(queries, i, remainingAndQuery(andRest)), true
+		}
+		seeks, ok := loginEqualitySeeksFromQuery(instanceID, qry)
+		if !ok {
+			continue
+		}
+		return seeks, spliceRemainingQuery(queries, i, nil), true
+	}
+	return nil, queries, false
+}
+
+func remainingAndQuery(rest []SearchQuery) SearchQuery {
+	switch len(rest) {
+	case 0:
+		return nil
+	case 1:
+		return rest[0]
+	default:
+		and, err := NewAndQuery(rest...)
+		if err != nil {
+			return nil
+		}
+		return and
+	}
+}
+
+func spliceRemainingQuery(queries []SearchQuery, i int, replacement SearchQuery) []SearchQuery {
+	n := len(queries) - 1
+	if replacement != nil {
+		n++
+	}
+	remaining := make([]SearchQuery, 0, n)
+	remaining = append(remaining, queries[:i]...)
+	if replacement != nil {
+		remaining = append(remaining, replacement)
+	}
+	remaining = append(remaining, queries[i+1:]...)
+	return remaining
+}
+
+func joinLoginEqualitySeeks(seeks []loginEqualitySeek) sq.Sqlizer {
+	parts := make([]string, len(seeks))
+	args := make([]interface{}, 0, len(seeks)*2)
+	for i, seek := range seeks {
+		parts[i] = seek.sql
+		args = append(args, seek.args...)
+	}
+	return sq.Expr(
+		"INNER JOIN ("+strings.Join(parts, " UNION ")+") AS matches ON "+UserIDCol.identifier()+" = matches.id",
+		args...,
+	)
+}

internal/query/user_login_name_exists_test.go

@@ -47,21 +47,33 @@ func TestNewUserLoginNameExistsQuery_ContainsFallsBackToView(t *testing.T) {
 	assert.Contains(t, strings.ToLower(sql), "login_name")
 }
 
-func TestExtractLoginNameEqualsFilter_TopLevel(t *testing.T) {
+func TestExtractLoginEqualitySeeks_LoginNameAndOrg(t *testing.T) {
 	loginNameQuery, err := NewUserLoginNameExistsQuery("[email protected]", TextEqualsIgnoreCase)
 	require.NoError(t, err)
 	orgQuery, err := NewUserResourceOwnerSearchQuery("org1", TextEquals)
 	require.NoError(t, err)
 
-	filter, remaining, ok := extractLoginNameEqualsFilter([]SearchQuery{loginNameQuery, orgQuery})
+	seeks, remaining, ok := extractLoginEqualitySeeks("inst-1", []SearchQuery{loginNameQuery, orgQuery})
 	require.True(t, ok)
-	require.NotNil(t, filter)
-	assert.Equal(t, "user", filter.username)
+	require.Len(t, seeks, 1)
+	assert.Contains(t, seeks[0].sql, "login_name_matches")
 	require.Len(t, remaining, 1)
 	assert.Equal(t, orgQuery, remaining[0])
 }
 
-func TestExtractLoginNameEqualsFilter_SkipsOrQuery(t *testing.T) {
+func TestNewUserEmailSearchQuery_EqualsIsLowerEqualsFilter(t *testing.T) {
+	qry, err := NewUserEmailSearchQuery("[email protected]", TextEquals)
+	require.NoError(t, err)
+	_, ok := qry.(*lowerEqualsFilter)
+	require.True(t, ok)
+
+	contains, err := NewUserEmailSearchQuery("Ada", TextContains)
+	require.NoError(t, err)
+	_, ok = contains.(*lowerEqualsFilter)
+	assert.False(t, ok)
+}
+
+func TestExtractLoginEqualitySeeks_OrLoginNameAndEmail(t *testing.T) {
 	loginNameQuery, err := NewUserLoginNameExistsQuery("[email protected]", TextEqualsIgnoreCase)
 	require.NoError(t, err)
 	emailQuery, err := NewUserEmailSearchQuery("[email protected]", TextEqualsIgnoreCase)
@@ -69,12 +81,45 @@ func TestExtractLoginNameEqualsFilter_SkipsOrQuery(t *testing.T) {
 	orQuery, err := NewOrQuery(loginNameQuery, emailQuery)
 	require.NoError(t, err)
 
-	_, remaining, ok := extractLoginNameEqualsFilter([]SearchQuery{orQuery})
+	seeks, remaining, ok := extractLoginEqualitySeeks("inst-1", []SearchQuery{orQuery})
+	require.True(t, ok)
+	require.Len(t, seeks, 2)
+	assert.Contains(t, seeks[0].sql, "login_name_matches")
+	assert.Contains(t, seeks[1].sql, "LOWER("+HumanEmailCol.identifier()+")")
+	assert.Empty(t, remaining)
+}
+
+func TestExtractLoginEqualitySeeks_EmptyOrArmDoesNotExtract(t *testing.T) {
+	emailQuery, err := NewUserEmailSearchQuery("", TextEqualsIgnoreCase)
+	require.NoError(t, err)
+	phoneQuery, err := NewUserPhoneSearchQuery("+41000000000", TextEquals)
+	require.NoError(t, err)
+	orQuery, err := NewOrQuery(emailQuery, phoneQuery)
+	require.NoError(t, err)
+
+	seeks, remaining, ok := extractLoginEqualitySeeks("inst-1", []SearchQuery{orQuery})
 	assert.False(t, ok)
+	assert.Nil(t, seeks)
 	require.Len(t, remaining, 1)
 	assert.Equal(t, orQuery, remaining[0])
 }
 
+func TestExtractLoginEqualitySeeks_NestedAndExtractsLoginName(t *testing.T) {
+	loginNameQuery, err := NewUserLoginNameExistsQuery("[email protected]", TextEqualsIgnoreCase)
+	require.NoError(t, err)
+	orgQuery, err := NewUserResourceOwnerSearchQuery("org1", TextEquals)
+	require.NoError(t, err)
+	andQuery, err := NewAndQuery(loginNameQuery, orgQuery)
+	require.NoError(t, err)
+
+	seeks, remaining, ok := extractLoginEqualitySeeks("inst-1", []SearchQuery{andQuery})
+	require.True(t, ok)
+	require.Len(t, seeks, 1)
+	assert.Contains(t, seeks[0].sql, "login_name_matches")
+	require.Len(t, remaining, 1)
+	assert.Equal(t, orgQuery, remaining[0])
+}
+
 func TestPrepareUsersQuery_LoginNameEqualsUsesIndexedJoin(t *testing.T) {
 	ctx := authz.WithInstanceID(t.Context(), "inst-1")
 	loginNameQuery, err := NewUserLoginNameExistsQuery("[email protected]", TextEqualsIgnoreCase)
@@ -138,7 +183,7 @@ func TestPrepareUsersQuery_LoginNameEqualsWithOrgFilter(t *testing.T) {
 	assert.Contains(t, args, "user")
 }
 
-func TestPrepareUsersQuery_LoginNameOrEmailDoesNotRewrite(t *testing.T) {
+func TestPrepareUsersQuery_LoginNameOrEmailUsesUnion(t *testing.T) {
 	ctx := authz.WithInstanceID(t.Context(), "inst-1")
 	loginNameQuery, err := NewUserLoginNameExistsQuery("[email protected]", TextEqualsIgnoreCase)
 	require.NoError(t, err)
@@ -151,11 +196,268 @@ func TestPrepareUsersQuery_LoginNameOrEmailDoesNotRewrite(t *testing.T) {
 		Queries: []SearchQuery{orQuery},
 	}
 	builder, _ := q.prepareUsersQuery(ctx, false)
+	sql, args, err := builder.ToSql()
+	require.NoError(t, err)
+
+	assert.Contains(t, sql, "UNION")
+	assert.Contains(t, sql, "AS matches")
+	assert.Contains(t, sql, "login_name_matches")
+	assert.Contains(t, sql, "login_names3_users")
+	assert.Contains(t, sql, "LOWER("+HumanEmailCol.identifier()+")")
+	assert.NotContains(t, sql, "login_name_lower")
+	assert.Contains(t, args, "[email protected]")
+}
+
+func TestPrepareUsersQuery_UsernameOrEmailUsesUnion(t *testing.T) {
+	ctx := authz.WithInstanceID(t.Context(), "inst-1")
+	usernameQuery, err := NewUserUsernameSearchQuery("user165000", TextEqualsIgnoreCase)
+	require.NoError(t, err)
+	emailQuery, err := NewUserEmailSearchQuery("[email protected]", TextEqualsIgnoreCase)
+	require.NoError(t, err)
+	orQuery, err := NewOrQuery(usernameQuery, emailQuery)
+	require.NoError(t, err)
+
+	q := &UserSearchQueries{
+		Queries: []SearchQuery{orQuery},
+	}
+	builder, _ := q.prepareUsersQuery(ctx, false)
+	sql, args, err := builder.ToSql()
+	require.NoError(t, err)
+
+	assert.Contains(t, sql, "UNION")
+	assert.Contains(t, sql, "AS matches")
+	assert.Contains(t, sql, "LOWER("+UserUsernameCol.identifier()+")")
+	assert.Contains(t, sql, "LOWER("+HumanEmailCol.identifier()+")")
+	assert.NotContains(t, sql, "login_name_matches")
+	assert.Contains(t, args, "user165000")
+	assert.Contains(t, args, "[email protected]")
+}
+
+func TestPrepareUsersQuery_EmailOrPhoneUsesUnion(t *testing.T) {
+	ctx := authz.WithInstanceID(t.Context(), "inst-1")
+	emailQuery, err := NewUserEmailSearchQuery("[email protected]", TextEqualsIgnoreCase)
+	require.NoError(t, err)
+	phoneQuery, err := NewUserPhoneSearchQuery("+41000000000", TextEquals)
+	require.NoError(t, err)
+	orQuery, err := NewOrQuery(emailQuery, phoneQuery)
+	require.NoError(t, err)
+
+	q := &UserSearchQueries{
+		Queries: []SearchQuery{orQuery},
+	}
+	builder, _ := q.prepareUsersQuery(ctx, false)
+	sql, args, err := builder.ToSql()
+	require.NoError(t, err)
+
+	assert.Contains(t, sql, "UNION")
+	assert.Contains(t, sql, "LOWER("+HumanEmailCol.identifier()+")")
+	assert.Contains(t, sql, "LOWER("+HumanPhoneCol.identifier()+")")
+	assert.Contains(t, args, "[email protected]")
+	assert.Contains(t, args, "+41000000000")
+}
+
+func TestPrepareUsersQuery_EmailEqualsRechecksExactColumn(t *testing.T) {
+	ctx := authz.WithInstanceID(t.Context(), "inst-1")
+	emailQuery, err := NewUserEmailSearchQuery("[email protected]", TextEquals)
+	require.NoError(t, err)
+
+	q := &UserSearchQueries{
+		Queries: []SearchQuery{emailQuery},
+	}
+	builder, _ := q.prepareUsersQuery(ctx, false)
+	sql, args, err := builder.ToSql()
+	require.NoError(t, err)
+
+	assert.Contains(t, sql, "AS matches")
+	assert.Contains(t, sql, "LOWER("+HumanEmailCol.identifier()+")")
+	assert.Contains(t, sql, "LOWER($")
+	assert.Contains(t, sql, HumanEmailCol.identifier()+" =")
+	assert.Contains(t, args, "[email protected]")
+	assert.NotContains(t, args, "[email protected]")
+}
+
+func TestPrepareUsersQuery_EmailIgnoreCaseDoesNotRecheckExactColumn(t *testing.T) {
+	ctx := authz.WithInstanceID(t.Context(), "inst-1")
+	emailQuery, err := NewUserEmailSearchQuery("[email protected]", TextEqualsIgnoreCase)
+	require.NoError(t, err)
+
+	q := &UserSearchQueries{
+		Queries: []SearchQuery{emailQuery},
+	}
+	builder, _ := q.prepareUsersQuery(ctx, false)
+	sql, args, err := builder.ToSql()
+	require.NoError(t, err)
+
+	assert.Contains(t, sql, "AS matches")
+	assert.Contains(t, sql, "LOWER("+HumanEmailCol.identifier()+")")
+	assert.NotContains(t, sql, "LOWER($")
+	assert.NotContains(t, sql, HumanEmailCol.identifier()+" =")
+	assert.Contains(t, args, "[email protected]")
+	assert.NotContains(t, args, "[email protected]")
+}
+
+func TestPrepareUsersQuery_PhoneIgnoreCaseUsesUnion(t *testing.T) {
+	ctx := authz.WithInstanceID(t.Context(), "inst-1")
+	phoneQuery, err := NewUserPhoneSearchQuery("+41000000000", TextEqualsIgnoreCase)
+	require.NoError(t, err)
+
+	q := &UserSearchQueries{
+		Queries: []SearchQuery{phoneQuery},
+	}
+	builder, _ := q.prepareUsersQuery(ctx, false)
+	sql, args, err := builder.ToSql()
+	require.NoError(t, err)
+
+	assert.Contains(t, sql, "AS matches")
+	assert.Contains(t, sql, "LOWER("+HumanPhoneCol.identifier()+")")
+	assert.Contains(t, args, "+41000000000")
+}
+
+func TestPrepareUsersQuery_ContainsDoesNotUseUnion(t *testing.T) {
+	ctx := authz.WithInstanceID(t.Context(), "inst-1")
+	usernameQuery, err := NewUserUsernameSearchQuery("user", TextContainsIgnoreCase)
+	require.NoError(t, err)
+
+	q := &UserSearchQueries{
+		Queries: []SearchQuery{usernameQuery},
+	}
+	builder, _ := q.prepareUsersQuery(ctx, false)
 	sql, _, err := builder.ToSql()
 	require.NoError(t, err)
 
-	assert.NotContains(t, sql, "login_name_matches")
-	assert.Contains(t, sql, "projections.login_names3")
+	assert.NotContains(t, sql, "AS matches")
+	assert.NotContains(t, sql, " UNION ")
+}
+
+func TestPrepareUsersQuery_DisplayNameDoesNotUseUnion(t *testing.T) {
+	ctx := authz.WithInstanceID(t.Context(), "inst-1")
+	displayNameQuery, err := NewUserDisplayNameSearchQuery("Ada Lovelace", TextEqualsIgnoreCase)
+	require.NoError(t, err)
+
+	q := &UserSearchQueries{
+		Queries: []SearchQuery{displayNameQuery},
+	}
+	builder, _ := q.prepareUsersQuery(ctx, false)
+	sql, _, err := builder.ToSql()
+	require.NoError(t, err)
+
+	assert.NotContains(t, sql, "AS matches")
+	assert.NotContains(t, sql, " UNION ")
+}
+
+func TestPrepareUsersQuery_UsernameOrContainsDoesNotUseUnion(t *testing.T) {
+	ctx := authz.WithInstanceID(t.Context(), "inst-1")
+	usernameQuery, err := NewUserUsernameSearchQuery("user165000", TextEqualsIgnoreCase)
+	require.NoError(t, err)
+	displayNameQuery, err := NewUserDisplayNameSearchQuery("user", TextContainsIgnoreCase)
+	require.NoError(t, err)
+	orQuery, err := NewOrQuery(usernameQuery, displayNameQuery)
+	require.NoError(t, err)
+
+	q := &UserSearchQueries{
+		Queries: []SearchQuery{orQuery},
+	}
+	builder, _ := q.prepareUsersQuery(ctx, false)
+	sql, _, err := builder.ToSql()
+	require.NoError(t, err)
+
+	assert.NotContains(t, sql, "AS matches")
+	assert.NotContains(t, sql, " UNION ")
+}
+
+func TestPrepareUsersQuery_UsernameOrUsernameUsesUnion(t *testing.T) {
+	ctx := authz.WithInstanceID(t.Context(), "inst-1")
+	alice, err := NewUserUsernameSearchQuery("alice", TextEqualsIgnoreCase)
+	require.NoError(t, err)
+	bob, err := NewUserUsernameSearchQuery("bob", TextEqualsIgnoreCase)
+	require.NoError(t, err)
+	orQuery, err := NewOrQuery(alice, bob)
+	require.NoError(t, err)
+
+	q := &UserSearchQueries{
+		Queries: []SearchQuery{orQuery},
+	}
+	builder, _ := q.prepareUsersQuery(ctx, false)
+	sql, args, err := builder.ToSql()
+	require.NoError(t, err)
+
+	assert.Contains(t, sql, "UNION")
+	assert.Contains(t, sql, "AS matches")
+	assert.Equal(t, 2, strings.Count(sql, "LOWER("+UserUsernameCol.identifier()+")"))
+	assert.Contains(t, args, "alice")
+	assert.Contains(t, args, "bob")
+}
+
+func TestPrepareUsersQuery_SiblingUsernameAndKeepsRemainingWhere(t *testing.T) {
+	ctx := authz.WithInstanceID(t.Context(), "inst-1")
+	alice, err := NewUserUsernameSearchQuery("alice", TextEqualsIgnoreCase)
+	require.NoError(t, err)
+	bob, err := NewUserUsernameSearchQuery("bob", TextEqualsIgnoreCase)
+	require.NoError(t, err)
+
+	q := &UserSearchQueries{
+		Queries: []SearchQuery{alice, bob},
+	}
+	builder, _ := q.prepareUsersQuery(ctx, false)
+	sql, args, err := builder.ToSql()
+	require.NoError(t, err)
+
+	assert.Contains(t, sql, "AS matches")
+	assert.NotContains(t, sql, " UNION ")
+	assert.Contains(t, args, "alice")
+	assert.Contains(t, args, "bob")
+}
+
+func TestPrepareUsersQuery_NestedAndOfOrUsesUnion(t *testing.T) {
+	ctx := authz.WithInstanceID(t.Context(), "inst-1")
+	alice, err := NewUserUsernameSearchQuery("alice", TextEqualsIgnoreCase)
+	require.NoError(t, err)
+	bob, err := NewUserUsernameSearchQuery("bob", TextEqualsIgnoreCase)
+	require.NoError(t, err)
+	orQuery, err := NewOrQuery(alice, bob)
+	require.NoError(t, err)
+	orgQuery, err := NewUserResourceOwnerSearchQuery("org1", TextEquals)
+	require.NoError(t, err)
+	andQuery, err := NewAndQuery(orQuery, orgQuery)
+	require.NoError(t, err)
+
+	q := &UserSearchQueries{
+		Queries: []SearchQuery{andQuery},
+	}
+	builder, _ := q.prepareUsersQuery(ctx, false)
+	sql, args, err := builder.ToSql()
+	require.NoError(t, err)
+
+	assert.Contains(t, sql, "AS matches")
+	assert.Contains(t, sql, " UNION ")
+	assert.Contains(t, sql, "resource_owner")
+	assert.Contains(t, args, "org1")
+	assert.Contains(t, args, "alice")
+	assert.Contains(t, args, "bob")
+}
+
+func TestPrepareUsersQuery_NestedOrOfAndDoesNotUseUnion(t *testing.T) {
+	ctx := authz.WithInstanceID(t.Context(), "inst-1")
+	alice, err := NewUserUsernameSearchQuery("alice", TextEqualsIgnoreCase)
+	require.NoError(t, err)
+	orgQuery, err := NewUserResourceOwnerSearchQuery("org1", TextEquals)
+	require.NoError(t, err)
+	andQuery, err := NewAndQuery(alice, orgQuery)
+	require.NoError(t, err)
+	bob, err := NewUserUsernameSearchQuery("bob", TextEqualsIgnoreCase)
+	require.NoError(t, err)
+	orQuery, err := NewOrQuery(andQuery, bob)
+	require.NoError(t, err)
+
+	q := &UserSearchQueries{
+		Queries: []SearchQuery{orQuery},
+	}
+	builder, _ := q.prepareUsersQuery(ctx, false)
+	sql, _, err := builder.ToSql()
+	require.NoError(t, err)
+
+	assert.NotContains(t, sql, "AS matches")
+	assert.NotContains(t, sql, " UNION ")
 }
 
 func TestPrepareUsersQuery_MetadataFilterKeepsDistinctJoin(t *testing.T) {