feat(app-host): load studio UI on homepage

- Build studio alongside app-host in build-vercel.sh
- Copy studio dist files to app-host public/ directory
- Add SPA routing to serve studio UI for non-API routes
- Add cache headers for static assets

Agent-Logs-Url: https://github.com/objectstack-ai/framework/sessions/13b58dad-d5c4-4665-b3dd-b92c8b773190

Co-authored-by: hotlong <50353452+hotlong@users.noreply.github.com>

Author: Claude

examples/app-host/scripts/build-vercel.sh

@@ -7,20 +7,33 @@ set -euo pipefail
 #   - api/[[...route]].js is committed to the repo (Vercel detects it pre-build)
 #   - esbuild bundles server/index.ts → api/_handler.js (self-contained bundle)
 #   - The committed .js wrapper re-exports from _handler.js at runtime
+#   - Studio SPA is built and copied to public/ for serving the UI
 #
 # Steps:
-#   1. Build the project with turbo
+#   1. Build the project with turbo (includes studio)
 #   2. Bundle the API serverless function (→ api/_handler.js)
-#   3. Copy native/external modules into local node_modules for Vercel packaging
+#   3. Copy studio dist files to public/ for UI serving
 
 echo "[build-vercel] Starting app-host build..."
 
 # 1. Build the project with turbo (from monorepo root)
+# This builds both app-host and studio
 cd ../..
-pnpm turbo run build --filter=@example/app-host
+pnpm turbo run build --filter=@example/app-host --filter=@objectstack/studio
 cd examples/app-host
 
 # 2. Bundle API serverless function
 node scripts/bundle-api.mjs
 
-echo "[build-vercel] Done. Serverless function in api/[[...route]].js → api/_handler.js"
+# 3. Copy studio dist files to public/ for UI serving
+echo "[build-vercel] Copying studio dist to public/..."
+rm -rf public
+mkdir -p public
+if [ -d "../../apps/studio/dist" ]; then
+  cp -r ../../apps/studio/dist/* public/
+  echo "[build-vercel]   ✓ Copied studio dist to public/"
+else
+  echo "[build-vercel]   ⚠ Studio dist not found (skipped)"
+fi
+
+echo "[build-vercel] Done. Static files in public/, serverless function in api/[[...route]].js → api/_handler.js"

examples/app-host/vercel.json

@@ -9,7 +9,16 @@
       "maxDuration": 60
     }
   },
+  "headers": [
+    {
+      "source": "/assets/(.*)",
+      "headers": [
+        { "key": "Cache-Control", "value": "public, max-age=31536000, immutable" }
+      ]
+    }
+  ],
   "rewrites": [
-    { "source": "/api/:path*", "destination": "/api/[[...route]]" }
+    { "source": "/api/:path*", "destination": "/api/[[...route]]" },
+    { "source": "/((?!api/).*)", "destination": "/index.html" }
   ]
 }