Show build server in build details

[arjunkomath]

Summary

• join the claiming server into build details and builds-list responses
• show linked branch by author on server attribution in build details and build rows
• require an authenticated session for both build data endpoints
• stop active-build polling once the latest build reaches a terminal status

Verification

• npx biome check --write on the changed web files
• ./node_modules/.bin/tsc --noEmit
• Oracle review completed; Drizzle left-join nullability, SWR server transitions, and build API authentication reviewed

Notes

• queued builds omit the server attribution until an agent claims the build
• no database or agent changes are required

[github-actions]

React Doctor found no issues. 🎉

⚠️ Warning: .github/workflows/react-doctor.yml is configured incorrectly. See below to fix.

React Doctor compares against main to report only the issues this pull request introduces. This run couldn't complete that comparison (usually a shallow CI checkout with no merge base), so it listed every issue in the changed files, including ones that already existed on main.

Add fetch-depth: 0 to the actions/checkout step in .github/workflows/react-doctor.yml so the checkout includes the history React Doctor needs:

 jobs:
   react-doctor:
     steps:
       - uses: actions/checkout@v5
+        with:
+          fetch-depth: 0

       - uses: millionco/react-doctor@v2

To silence this warning, set silence-missing-baseline-warning: true on the React Doctor action.

_{Reviewed by React Doctor for commit c13a7b8.}