Fix Studio server mode for app-host Vercel deployment

[Claude]

Studio was running in MSW mode after deploying app-host to Vercel, instead of connecting to the API server. The issue was that VITE_RUNTIME_MODE=server was not being set during the build process.

Changes

• Add build.env to examples/app-host/vercel.json: Set VITE_RUNTIME_MODE=server and VITE_SERVER_URL="" to configure Studio in server mode during Vite build
• Update deployment documentation: Document build environment variables and add troubleshooting section for Studio MSW mode issues

Technical Context

Vite embeds environment variables at build time. The standalone Studio deployment (apps/studio/vercel.json) already had this configuration:

"build": {
  "env": {
    "VITE_RUNTIME_MODE": "server",
    "VITE_SERVER_URL": ""
  }
}

The app-host deployment was missing this section, causing Studio to default to MSW mode regardless of the .env.production file (which is only used during local builds, not Vercel builds).

[vercel]

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Project	Deployment	Actions	Updated (UTC)
objectstack-demo	Ready	Preview, Comment	Apr 14, 2026 7:01am
objectstack-play	Ready	Preview, Comment	Apr 14, 2026 7:01am
spec	Ready	Preview, Comment	Apr 14, 2026 7:01am