fix: copy API serverless function into output directory for Vercel detection

Vercel's `framework: null` defaults outputDirectory to `public/` when that
directory exists and only detects serverless functions INSIDE the output
directory.  The bundled `api/index.js` was at the project root (outside
`public/`) so Vercel never recognised it — all `/api/*` routes fell through
to the SPA catch-all and returned `index.html`.

Added step 4 to `build-vercel.sh` that copies `api/index.js` into
`public/api/` after the SPA files are placed in `public/`.  This ensures
Vercel detects it as a serverless function within the output directory.

Agent-Logs-Url: https://github.com/objectstack-ai/framework/sessions/85727540-2aac-406e-83f5-790a0c650da3

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

Author: Copilot

CHANGELOG.md

@@ -9,11 +9,15 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 
 ### 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 and the `api/` directory is auto-detected for serverless
-  functions.  Removed the `functions` block (the in-code `export const config`
-  in `server/index.ts` already configures memory/maxDuration without pre-build
+  `apps/studio/scripts/build-vercel.sh` to copy the bundled serverless function
+  (`api/index.js`) into the output directory (`public/api/`).  Vercel's
+  `framework: null` defaults `outputDirectory` to `public/` when that directory
+  exists, and only detects serverless functions **inside** the output directory.
+  Previously `api/index.js` was generated at the project root (outside `public/`)
+  and Vercel never recognised it, causing all `/api/*` routes to fall through to
+  the SPA catch-all rewrite.  Also set `outputDirectory: "public"` explicitly in
+  `vercel.json` for clarity, and removed the `functions` block (the in-code
+  `export const config` already configures memory/maxDuration without pre-build
   file-pattern validation errors).
 - **Studio CORS error on Vercel temporary/preview domains** — Changed
   `VITE_SERVER_URL` from hardcoded `https://play.objectstack.ai` to `""`

apps/studio/scripts/build-vercel.sh

@@ -3,13 +3,15 @@ set -euo pipefail
 
 # Build script for Vercel deployment of @objectstack/studio.
 #
-# Without outputDirectory, Vercel serves static files from public/.
-# Serverless functions are detected from api/ at the project root.
+# Vercel uses outputDirectory (vercel.json → "public") for BOTH static files
+# and serverless function detection.  The api/ subdirectory MUST be inside
+# the output directory — files at the project root are ignored.
 #
 # Steps:
 #   1. Turbo build (Vite SPA → dist/)
 #   2. Bundle the API serverless function (→ api/index.js)
 #   3. Copy Vite output to public/ for Vercel CDN serving
+#   4. Copy API function into public/api/ so Vercel detects it
 
 echo "[build-vercel] Starting studio build..."
 
@@ -26,4 +28,11 @@ rm -rf public
 mkdir -p public
 cp -r dist/* public/
 
-echo "[build-vercel] Done. Static files in public/, serverless function in api/index.js"
+# 4. Copy API function into output directory for Vercel detection
+#    Vercel only looks for serverless functions inside outputDirectory.
+#    Without this step, api/index.js at the project root is invisible.
+mkdir -p public/api
+cp api/index.js public/api/
+cp api/index.js.map public/api/ 2>/dev/null || true
+
+echo "[build-vercel] Done. Static files + API function in public/"