[BUG] Cowork task list desynced from assistant's tool view; app restart made it worse

### Preflight Checklist

- [x] I have searched [existing issues](https://github.com/anthropics/claude-code/issues?q=is%3Aissue%20state%3Aopen%20label%3Abug) 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?

In a Cowork session, the task list became desynchronized between what I (the user) see in the UI and what the assistant can access via its task tool (list/get/update).

The assistant's tool calls sometimes returned 0 tasks or "task not found" for entries that were clearly visible and confirmed in my UI.
On my suggestion, we tried restarting the Claude desktop app to fix this. Instead, it made things worse: 2 of 4 tasks disappeared from my UI entirely.
The assistant recreated the missing tasks from conversation context, which restored the correct 4 entries in my UI (no duplicates), but the assistant still cannot access the original items (one open, one completed) via its own tool — meaning in a future session it would have no way to know what was previously discussed about them, since the task list is meant to persist that information, not just live in chat history.

This looks like a real sync/persistence bug between the task-list backend and the assistant's tool interface, not just a UI glitch.

### What Should Happen?

task list should always be synchronized between what the user sees in the UI and what the assistant can access via its task tool

### Error Messages/Logs

```shell

```

### Steps to Reproduce

In a long-running Cowork chat session, use the task list feature over multiple turns: create several tasks, mark some as completed, update others.
At some point (unclear exact trigger), the assistant's task tool calls (list/get) stop returning some tasks that are still visible in my UI — including a task the assistant itself created and updated earlier in the same session, and a task I had just confirmed was visible on my end.
Note: a task ID that worked for one tool call (e.g. updating its description) sometimes failed on the very next call for the same ID ("task not found"), suggesting some kind of mid-session ID reset/renumbering.
Restart the Claude desktop app while in this desynced state.
Observe: instead of resolving the mismatch, the restart causes 2 of 4 tasks to disappear from the UI entirely (data loss, not just a display glitch — they don't reappear on reload).

Expected behavior: The assistant's task tool and the user-facing task list UI should always reflect the same underlying data; an app restart should never cause tasks to be lost.

Actual behavior: Tool-side and UI-side views diverge over the course of a session, and restarting the app made it worse rather than fixing it.

I don't have a minimal/isolated repro (e.g. exact number of turns or specific actions that trigger it) — this surfaced organically in a long working session, not from a small test case.

### Claude Model

Sonnet (default)

### Is this a regression?

No, this never worked

### Last Working Version

_No response_

### Claude Code Version

Claude 1.46388.3 (f1b512) 2026-09-04T14:20:14.000Z

### Platform

Other

### Operating System

macOS

### Terminal/Shell

Terminal.app (macOS)

### Additional Information

_No response_

Start with the Cowork task-list UI and the assistant's task-tool entry points, then trace how task IDs and persisted data are shared between them. Reproduce the mismatch in a long-running session and after an app restart, using the reported list/get/update failures and disappearing tasks as the checks for completion.

索引モデルが issue の本文から書いたものです。