[BUG] Cowork: renaming a scheduled task doesn't persist — reverts to old name on restart

Summary

Renaming a Cowork scheduled task updates the name shown in the session header, but the change is never written to storage: the Scheduled list in the sidebar keeps the old name, and after an app restart the header reverts to the old name too. The rename behaves like a transient, UI-only label.

Environment

• Claude Desktop, Windows 11 (MSIX build, package Claude_pzs8sxrjxfjjc)
• Cowork tab, a scheduled (Daily) task under a project

Steps to reproduce

1. Open a Cowork scheduled task.
2. Rename it via the header dropdown (e.g. Bubba school shoe watch → Bubba Boots).
3. Note the header shows the new name, but the Scheduled list in the left sidebar still shows the old name.
4. Also try renaming from the Scheduled list item itself.
5. Restart Claude Desktop.

Expected

New name persists everywhere (header + Scheduled list) and survives restart.

Actual

• Scheduled list never updates (old name).
• Renaming from the Scheduled list also does not persist.
• After restart the header reverts to the old name.

Additional detail (on-disk verification)

The session record on disk still holds the OLD name after the rename:
...\LocalCache\Roaming\Claude\local-agent-mode-sessions\<id>\<sub>\local_<uuid>.json → the "title" field is unchanged. So the rename never writes to the session record; the new name only exists as a transient in-memory header label.

Related

Appears to be the same state-persistence family as #45097 (Cowork custom instructions revert on restart) and #61648 (scheduled-task preference reset on startup).