[BUG] Stale background tasks shown as permanently "running" (200+ hours), survive Clear and full PC restart

Preflight Checklist

• [x] I have searched existing issues and this hasn't been reported yet
• [x] This is a single bug report (please file separate reports for different bugs)
• [x] I am using the latest version of Claude Code

What's Wrong?

The "Background Tasks" panel shows old tasks from unrelated past sessions as still "Running" (200+ hours elapsed), and Claude Code chat itself is unresponsive — no chat produces any response. This started on first launch after login on a freshly installed instance.

What Should Happen?

Completed/orphaned background tasks should not be shown as "Running" indefinitely, and should not block chat from responding.

Error Messages/Logs

No error message shown. See attached screenshots of the Background Tasks panel showing:
- "Start local server to verify answer sheet" — running 213h59m42s
- "Locate the xlsx skill's recalc.py validation script" — running 271h50m35s (this task is known to have already completed successfully in the originating session)

Steps to Reproduce

1. Have background bash tasks run in a Claude Code session on one PC/session under an account
2. Let a task finish (receive a completion notification in that session)
3. Install Claude desktop app fresh on a different Windows PC, log in with the same account
4. Open the Background Tasks panel — the already-finished task is still shown as "Running" with an ever-increasing timer
5. Chat does not respond to any input

<img width="619" height="482" alt="Image" src="https://github.com/user-attachments/assets/9aa7014d-103c-418e-a32b-01fd659cdbe0" />
<img width="579" height="343" alt="Image" src="https://github.com/user-attachments/assets/b77ddc6b-60a8-41c5-a47a-eef920c7b4bc" />

Claude Model

Sonnet (default)

Is this a regression?

Yes, this worked in a previous version

Last Working Version

_No response_

Claude Code Version

2.1.221 (unable to verify on affected PC — chat unresponsive)

Platform

Anthropic API

Operating System

Windows

Terminal/Shell

Windows Terminal

Additional Information

_No response_