fix(frontend): proxy /api and /sitemap.xml at runtime, not via baked rewrites

next.config.js rewrites() bakes its destination into the build
(routes-manifest.json), capturing FASTAPI_URL at build time. Because one
frontend image is promoted staging->prod, the baked backend host forced
every environment to name the backend service identically; staging names
it 'backend_stg', so the browser's /api/* calls proxied to the baked
'http://backend' and failed with getaddrinfo ENOTFOUND backend. (SSR was
unaffected because lib/api.ts reads FASTAPI_URL at runtime.)

Replace the rewrites with route handlers that read FASTAPI_URL per
request:
- app/api/[...path]/route.ts — transparent proxy for all methods, streams
  the response, strips hop-by-hop headers, and returns 502 on upstream
  failure instead of crashing.
- app/sitemap.xml/route.ts — proxies the backend sitemap (robots.ts points
  crawlers here).

The same promoted image now adapts to whatever the backend is called in
each environment. Verified: production build succeeds with /api/[...path]
and /sitemap.xml as dynamic routes and an empty rewrites manifest.

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

nextjs-app/next.config.js

@@ -3,21 +3,10 @@ const nextConfig = {
   // Enable standalone output for Docker
   output: 'standalone',
 
-  // API Proxy to FastAPI backend
-  async rewrites() {
-    const apiUrl = process.env.FASTAPI_URL || 'http://localhost:8000/api';
-    const backendUrl = apiUrl.replace(/\/api$/, '');
-    return [
-      {
-        source: '/api/:path*',
-        destination: `${apiUrl}/:path*`,
-      },
-      {
-        source: '/sitemap.xml',
-        destination: `${backendUrl}/sitemap.xml`,
-      },
-    ];
-  },
+  // The /api/* and /sitemap.xml proxies to the FastAPI backend are route
+  // handlers (app/api/[...path]/route.ts, app/sitemap.xml/route.ts) rather
+  // than rewrites, so the backend host is read from FASTAPI_URL at runtime
+  // instead of being baked into the build.
 
   // Image optimization
   images: {