[BUG] Cowork task starts with no device_* tools while the bridge is authenticated (Windows 10 22H2, after KB5129236)

### 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?

Every newly created Cowork task starts WITHOUT the device_* tool layer (no device_bash, device_list_dir, device_stage_files, device_commit_files). The session lands in a cloud container only (hostname `vm`, cwd `/`, empty /mnt/user-data/uploads) and stays that way for its entire lifetime. The assistant reports it simply has no device_* tools available.

This is NOT the September 8 Plan9 share regression (status incident "Degraded functionality for Claude Cowork on Windows", resolved). Under that bug the device_* tools were PRESENT and mounting failed. Here the tools are never registered at all, while the bridge reports a healthy connection.

### What Should Happen?

A task created while `remote-tools-device` is authenticated should expose the device_* tools and reach the local working folder.

### Error Messages/Logs

```shell
No error is shown anywhere in the UI. main.log shows a normal, successful bridge handshake:

2026-09-16 15:53:11 [info] [remote-tools-device] connecting DO bridge with: get_device_info, device_list_dir, device_stage_files, device_commit_files, ..., device_bash, computer_*, project_memory_read, project_memory_write (+0 grand-prix, +14 local-mcp, +0 direct-mcp)
2026-09-16 15:53:11 [info] [remote-tools-device] close
2026-09-16 15:53:12 [info] [remote-tools-device] connecting DO bridge with:
2026-09-16 15:53:12 [info] [remote-tools-device] connect frame sent: device_id keyed
2026-09-16 15:53:12 [info] [remote-tools-device] authenticated
2026-09-16 16:00:11 [info] [remote-tools-device] socket closed: 1006
2026-09-16 16:00:11 [info] [remote-tools-device] reconnect #1 in 3588ms
2026-09-16 16:00:15 [info] [remote-tools-device] authenticated
2026-09-16 16:00:17 [info] [remote-tools-device] socket closed: 1006
2026-09-16 16:00:17 [info] [remote-tools-device] reconnect #2 in 1464ms
2026-09-16 16:00:25 [info] [remote-tools-device] authenticated

Two secondary observations:
1. The 1006 closures come after ~7 minutes of idle time, then again after 2 seconds. Network path is clean (see below), so this looks like a server-side or client-side idle handling problem.
2. `device_request_folder_access` never appears in the log when a task is created, which may mean the task is never bound to the device at all.

Full excerpt attached.
```

### Steps to Reproduce

1. Windows 10 22H2, build 19045.7727, KB5129236 installed.
2. Kill every Claude process, relaunch the app.
3. Tail main.log and wait for `[remote-tools-device] authenticated`.
4. With the tail still running and showing no disconnects, create a BRAND NEW Cowork task.
5. Ask the assistant to run `device_bash` with `hostname && pwd`.
6. Result: the assistant reports no device_* tools exist in the session. Repeats every time.

### Claude Model

Opus

### Is this a regression?

I don't know

### Last Working Version

_No response_

### Claude Code Version

-

### Platform

Anthropic API

### Operating System

Windows

### Terminal/Shell

Terminal.app (macOS)

### Additional Information

### Environment
- OS: Windows 10 22H2, build 19045.7727
- Claude Desktop version:
- Package:
- Plan:
- vp9fs.dll: 10.0.19041.7727
- Log path: %LOCALAPPDATA%\Packages\Claude_pzs8sxrjxfjjc\LocalCache\Local\Claude\Logs\main.log

### Impact
Cowork is unusable for local repository work. The previously documented workaround (shipping the repo as an archive) does not apply here, because it relied on device_stage_files / device_commit_files, which are also missing.

[cowork-bridge-excerpt.log](https://github.com/user-attachments/files/32299743/cowork-bridge-excerpt.log)

Start by reproducing the issue on Windows 10 22H2 while tailing main.log at %LOCALAPPDATA%\Packages\Claude_pzs8sxrjxfjjc\LocalCache\Local\Claude\Logs\main.log. Compare the authenticated remote-tools-device bridge state with a newly created Cowork task, including whether device_request_folder_access appears. Done means the task exposes the device_* tools and reaches the local working folder.

Written by the indexing model from the issue text.