feat(docs): add sitemap, robots, and metadataBase for SEO

Search Console had nothing to crawl: the site served no /sitemap.xml
or /robots.txt and metadata used relative URLs.

- app/sitemap.ts: enumerate all Fumadocs pages across the 7 locales
  with hreflang + x-default alternates (default-locale prefix hidden)
- app/robots.ts: allow all, declare the sitemap, disallow /api and
  the generated llms*.txt text dumps
- layout.tsx: set metadataBase so canonical/OG URLs are absolute

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

Author: os-zhuang

apps/docs/app/layout.tsx

@@ -3,6 +3,7 @@ import type { ReactNode } from 'react';
 import type { Metadata } from 'next';
 
 export const metadata: Metadata = {
+  metadataBase: new URL('https://docs.objectos.ai'),
   title: {
     template: '%s | ObjectOS',
     default: 'ObjectOS',

apps/docs/app/robots.ts

@@ -0,0 +1,18 @@
+import type { MetadataRoute } from 'next';
+
+const BASE = 'https://docs.objectos.ai';
+
+export const revalidate = false;
+
+export default function robots(): MetadataRoute.Robots {
+  return {
+    rules: {
+      userAgent: '*',
+      allow: '/',
+      // Generated text endpoints duplicate page content; keep them out of the index.
+      disallow: ['/api/', '/llms.txt', '/llms-full.txt'],
+    },
+    sitemap: `${BASE}/sitemap.xml`,
+    host: BASE,
+  };
+}

apps/docs/app/sitemap.ts

@@ -0,0 +1,60 @@
+import type { MetadataRoute } from 'next';
+import { source } from '@/lib/source';
+import { i18n } from '@/lib/i18n';
+
+// Canonical production host. Keep in sync with middleware's domain redirect.
+const BASE = 'https://docs.objectos.ai';
+
+// Build an absolute URL for a given locale, hiding the prefix for the
+// default language (matches i18n.hideLocale = 'default-locale').
+function localize(lang: string, path: string): string {
+  const suffix = path ? `/${path}` : '';
+  return lang === i18n.defaultLanguage
+    ? `${BASE}${suffix}`
+    : `${BASE}/${lang}${suffix}`;
+}
+
+// hreflang alternates map for a logical path, linking every locale version
+// plus an x-default that points at the English (canonical) URL.
+function alternates(path: string): Record<string, string> {
+  const languages: Record<string, string> = {};
+  for (const lang of i18n.languages) {
+    languages[lang] = localize(lang, path);
+  }
+  languages['x-default'] = localize(i18n.defaultLanguage, path);
+  return languages;
+}
+
+export const revalidate = false;
+
+export default function sitemap(): MetadataRoute.Sitemap {
+  const entries: MetadataRoute.Sitemap = [];
+
+  // Top-level static pages (paths are locale-independent slugs).
+  const staticPaths: Array<{ path: string; priority: number }> = [
+    { path: '', priority: 1 },
+    { path: 'download', priority: 0.6 },
+    { path: 'privacy', priority: 0.3 },
+    { path: 'terms', priority: 0.3 },
+  ];
+
+  // Documentation pages, enumerated from the Fumadocs source. Slugs are the
+  // same across locales, so we reconstruct each locale URL from page.slugs.
+  const docPaths = source
+    .getPages()
+    .map((page) => ({ path: ['docs', ...page.slugs].join('/'), priority: 0.8 }));
+
+  for (const { path, priority } of [...staticPaths, ...docPaths]) {
+    const langAlternates = alternates(path);
+    for (const lang of i18n.languages) {
+      entries.push({
+        url: localize(lang, path),
+        changeFrequency: 'weekly',
+        priority,
+        alternates: { languages: langAlternates },
+      });
+    }
+  }
+
+  return entries;
+}