fix: configure Vercel to serve API routes as serverless functions instead of HTML

- Add outputDirectory: "public" to vercel.json
- Add functions block declaring api/index.js as serverless function
- Fix API rewrite destination from /api to /api/index.js
- Update CHANGELOG.md

Agent-Logs-Url: https://github.com/objectstack-ai/spec/sessions/d0116abe-0010-46e2-a25d-08bc5236156b

Co-authored-by: xuyushun441-sys <255036401+xuyushun441-sys@users.noreply.github.com>

Author: Copilot

CHANGELOG.md

@@ -8,6 +8,12 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 ## [Unreleased]
 
 ### Fixed
+- **Studio Vercel API routes returning HTML instead of JSON** — Updated
+  `apps/studio/vercel.json` to correctly configure Vercel serverless functions.
+  Added `outputDirectory: "public"` so Vercel serves static files from the
+  correct directory, declared `api/index.js` in the `functions` block so Vercel
+  recognises it as a serverless function, and changed the API rewrite destination
+  from `/api` to `/api/index.js` to route requests to the bundled handler.
 - **Client test aligned with removed `ai.chat` method** — Updated
   `@objectstack/client` test suite to match the current API surface where
   `ai.chat()` was removed in favour of the Vercel AI SDK `useChat()` hook.

apps/studio/vercel.json

@@ -3,6 +3,13 @@
   "framework": null,
   "installCommand": "cd ../.. && pnpm install",
   "buildCommand": "bash scripts/build-vercel.sh",
+  "outputDirectory": "public",
+  "functions": {
+    "api/index.js": {
+      "memory": 1024,
+      "maxDuration": 60
+    }
+  },
   "build": {
     "env": {
       "VITE_RUNTIME_MODE": "server",
@@ -18,7 +25,7 @@
     }
   ],
   "rewrites": [
-    { "source": "/api/(.*)", "destination": "/api" },
+    { "source": "/api/(.*)", "destination": "/api/index.js" },
     { "source": "/((?!api/).*)", "destination": "/index.html" }
   ]
 }