chore(agents): add agents files (#11497)

apps/api/AGENTS.md

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+# ZITADEL API App Guide for AI Agents
+
+## Context
+The **API App** (`apps/api`) is the Nx application target for building and running the Go backend. Most backend implementation lives in `internal/`, while this project orchestrates build, generate, lint, and test workflows.
+
+## Source of Truth
+- **Go Toolchain**: Inspect root `go.mod` before Go work.
+- **API Design Contract**: Follow `API_DESIGN.md` for service and resource conventions.
+- **Domain Logic Location**: For implementation details, also read `internal/AGENTS.md`.
+
+## Verified Nx Targets
+- **Run API (prod profile)**: `pnpm nx run @zitadel/api:prod`
+- **Build**: `pnpm nx run @zitadel/api:build`
+- **Generate (all)**: `pnpm nx run @zitadel/api:generate`
+- **Lint**: `pnpm nx run @zitadel/api:lint`
+- **Test (all)**: `pnpm nx run @zitadel/api:test`
+- **Test (unit)**: `pnpm nx run @zitadel/api:test-unit`
+- **Test (integration)**: `pnpm nx run @zitadel/api:test-integration`
+
+## Generation Notes
+- `@zitadel/api:generate` can update generated, tracked files (stubs/assets/statik). Run it intentionally.
+- API changes in `proto/` often require regenerating API, package, and docs artifacts.

apps/docs/AGENTS.md

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+# ZITADEL Docs Guide for AI Agents
+
+## Context
+The **Docs App** (`apps/docs`) hosts the ZITADEL documentation. It has recently migrated to **Fumadocs**.
+
+## Key Technology
+- **Framework**: Fumadocs (built on Next.js).
+- **Content**: MDX (Markdown + React Components).
+- **Orchestration**: Nx.
+
+## Content Conventions
+- **Frontmatter**: Ensure standard Fumadocs frontmatter is used (title, description).
+- **Links**: Use absolute paths or standard MDX linking.
+- **Components**: Use only MDX components that are documented in the official Fumadocs MDX component reference and any project-specific MDX component documentation in this repo; do not introduce or rely on undocumented components.
+- **API Docs**: Changes in `proto/` or API response schemas often require regeneration via docs generation targets.
+
+## Verified Nx Targets
+- **Dev Server**: `pnpm nx run @zitadel/docs:dev`
+- **Build**: `pnpm nx run @zitadel/docs:build`
+- **Generate**: `pnpm nx run @zitadel/docs:generate`
+- **Lint**: `pnpm nx run @zitadel/docs:lint`
+- **Check Links**: `pnpm nx run @zitadel/docs:check-links`
+- **Check Types**: `pnpm nx run @zitadel/docs:check-types`
+- **Test**: `pnpm nx run @zitadel/docs:test`

apps/login/AGENTS.md

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+# ZITADEL Login App Guide for AI Agents
+
+## Context
+The **Login App** (`apps/login`) provides the user interface for authentication flows (Login, Register, MFA, etc.). It is built with Next.js and React.
+
+## Key Technology
+- **Framework**: Next.js (React).
+- **Styling**: TailwindCSS, configured via `apps/login/tailwind.config.mjs`.
+- **Data Fetching**: Primarily server-side interaction with ZITADEL APIs via `@zitadel/client` or direct gRPC calls where applicable.
+- **Language**: TypeScript.
+
+## Architecture & Conventions
+- **Routing**: Uses the Next.js App Router (routes are defined under `src/app/`).
+- **Composability**: Components should be small and reusable.
+- **State**: Critical authentication state is often managed via URL parameters (Auth Requests) and cookies/sessions.
+- **Scope Rule**: For shared API typings and client behavior, also read `packages/AGENTS.md` and `proto/AGENTS.md`.
+
+## Verified Nx Targets
+- **Dev Server**: `pnpm nx run @zitadel/login:dev`
+- **Build**: `pnpm nx run @zitadel/login:build`
+- **Lint**: `pnpm nx run @zitadel/login:lint`
+- **Test (all)**: `pnpm nx run @zitadel/login:test`
+- **Test (unit)**: `pnpm nx run @zitadel/login:test-unit`
+- **Test (integration)**: `pnpm nx run @zitadel/login:test-integration`