Add regression test for daemon disconnect after per-turn site check

[sejas]

Related issues

• Related to https://linear.app/a8c/issue/STU-2034/studio-code-desktop-messages-get-stuck
• Related to https://linear.app/a8c/issue/STU-2040 (fixed by Studio Code: Close daemon socket after per-turn site status check so headless runs can exit #4175)

Studio Code Desktop sessions got stuck in the "working" state after every response (STU-2034/STU-2040): a per-turn site running-state check left a daemon socket open, so the headless CLI child never exited and the UI never received the run-completion signal. #4175 fixed it by closing the socket after the check.

How AI was used in this PR

AI was used to investigate the root cause of the stuck-message bug (trace the run lifecycle and git history) and to draft the regression test. The test was reviewed and mutation-verified locally.

Proposed Changes

Add a test to avoid regressions that fails if that disconnect is ever removed again, so the same hang cannot silently return.

Testing Instructions

• Run npm test -- apps/cli/commands/ai/tests/index.test.ts — all tests pass.
• To confirm the test guards the regression: comment out the await disconnectFromDaemon(); line in apps/cli/commands/ai/index.ts (after the isSiteRunning check) and re-run — the new test fails.

Pre-merge Checklist

• Have you checked for TypeScript, React or other console errors?

[youknowriad]

Thanks for the test :)