perf: optimize docs static generation cost (#12108)

## Summary
- Switch the docs catch-all route to full static generation and prebuild
both latest and versioned docs paths.
- Prebuild OG images for all docs pages, make sitemap and LLM export
static, and remove nondeterministic sitemap timestamps.
- Reduce build-time overhead by memoizing docs sidebar trees and
skipping processed markdown generation for versioned docs.

## Testing
- `pnpm nx run @zitadel/docs:build`
- `pnpm nx run @zitadel/docs:lint`
- `pnpm nx run @zitadel/docs:check-types`
- Verified the prerender manifest contains 8,816 prerendered routes,
3,293 versioned docs routes, 4,406 OG routes, and zero revalidating docs
routes.

apps/docs/app/[[...slug]]/layout.tsx

@@ -1,69 +1,61 @@
-import { source, versionSource } from '@/lib/source';
+import { getAllDocPages, source, versionSource } from '@/lib/source';
 import { ReactNode } from 'react';
 import { DocsLayout } from 'fumadocs-ui/layouts/docs';
 import { baseOptions } from '@/lib/layout.shared';
 import { buildCustomTree } from '@/lib/custom-tree';
 import rawVersions from '@/content/versions.json';
- 
-const versions = rawVersions as any[];
 import { VersionSelector } from '@/components/version-selector';
 
+type DocVersion = { param: string };
+type PageTree = typeof source.pageTree;
+
+const versions = rawVersions as DocVersion[];
+const versionParams = new Set(versions.map((version) => version.param));
+
+const labelsMap = new Map<string, string>();
+for (const page of getAllDocPages()) {
+  if (page.data.sidebar_label) {
+    labelsMap.set(page.url, page.data.sidebar_label);
+  }
+}
+
+const latestTree = buildCustomTree(source.pageTree, { labels: labelsMap });
+const versionTreeCache = new Map<string, PageTree>();
+
+function getVersionTree(currentVersion: string): PageTree {
+  const cached = versionTreeCache.get(currentVersion);
+  if (cached) return cached;
+
+  const children = (versionSource.pageTree as any).children || [];
+  const versionFolder = children.find((node: any) => {
+    if (node.type !== 'folder') return false;
+    if (node.index?.url && node.index.url.includes(`/${currentVersion}`)) return true;
+    return Boolean(node.children?.[0]?.url?.includes(`/${currentVersion}`));
+  });
+
+  const tree = versionFolder
+    ? buildCustomTree(
+        {
+          name: versionFolder.name,
+          children: versionFolder.children,
+        } as any,
+        {
+          stripPrefix: `/${currentVersion}`,
+          labels: labelsMap,
+        },
+      )
+    : buildCustomTree(versionSource.pageTree, { labels: labelsMap });
+
+  versionTreeCache.set(currentVersion, tree);
+  return tree;
+}
+
 export default async function Layout(props: { children: ReactNode; params: Promise<{ slug?: string[] }> }) {
   const params = await props.params;
   const slug = params.slug || [];
 
-  // Determine current version and tail path
-  // If first slug segment matches a version param (e.g. v4.10), that's the version.
-  // Otherwise it's latest.
-  const versionParam = slug[0] && versions.find(v => v.param === slug[0]) ? slug[0] : undefined;
-  const currentVersion = versionParam || 'latest';
-
-  const allPages = [...source.getPages(), ...versionSource.getPages()];
-  const labelsMap = new Map<string, string>();
-  allPages.forEach(p => {
-    if (p.data.sidebar_label) {
-      labelsMap.set(p.url, p.data.sidebar_label);
-    }
-  });
-
-  let tree: typeof source.pageTree;
-  if (currentVersion !== 'latest') {
-    // Hoist the version folder to root to flatten sidebar
-    // versionSource.pageTree -> [ v4.10 folder, v4.9 folder ... ]
-    // We want the children of the specific version folder.
-     
-    const children = (versionSource.pageTree as any).children || [];
-
-    const versionFolder = children.find((node: any) => {
-      if (node.type !== 'folder') return false;
-      // Check if the folder's index page belongs to this version
-      if (node.index?.url && node.index.url.includes(`/${currentVersion}`)) return true;
-      // Fallback: check first child if index missing
-      if (node.children?.[0]?.url?.includes(`/${currentVersion}`)) return true;
-      return false;
-    });
-
-    if (versionFolder) {
-      // Hoist children
-      const hoistedTree = {
-        name: versionFolder.name,
-        children: versionFolder.children,
-      } as any;
-
-      // Apply custom sidebar structure (from local sidebar-data.ts)
-      // We strip the prefix '/v4.10' so the lookup matches generic keys 'guides/...'
-      // The logs showed the URLs start with /[version] not /docs/[version]
-      const prefix = currentVersion === 'latest' ? '/docs' : `/${currentVersion}`;
-      tree = buildCustomTree(hoistedTree, {
-        stripPrefix: prefix,
-        labels: labelsMap
-      });
-    } else {
-      tree = buildCustomTree(versionSource.pageTree, { labels: labelsMap });
-    }
-  } else {
-    tree = buildCustomTree(source.pageTree, { labels: labelsMap });
-  }
+  const currentVersion = slug[0] && versionParams.has(slug[0]) ? slug[0] : 'latest';
+  const tree = currentVersion === 'latest' ? latestTree : getVersionTree(currentVersion);
 
   return (
     <DocsLayout

apps/docs/app/[[...slug]]/page.tsx

@@ -1,4 +1,4 @@
-import { getPageImage, getPage, source } from '@/lib/source';
+import { generateAllDocParams, getPageImage, getPage, source } from '@/lib/source';
 import {
   DocsBody,
   DocsPage,
@@ -43,7 +43,7 @@ export const revalidate = false;
 export const dynamic = 'force-static';
 
 export async function generateStaticParams() {
-  return source.generateParams();
+  return generateAllDocParams();
 }
 
 export async function generateMetadata(