[BUG] Session breadcrumb shows stale project name from first-ever session

### 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?

The session breadcrumb/title bar in Claude Code Desktop permanently shows the name of the first project folder ever opened, regardless of which project is subsequently selected.

### What Should Happen?

The breadcrumb should update to reflect the currently active project folder.

### Error Messages/Logs

```shell

```

### Steps to Reproduce

1. Open Claude Code Desktop and select any project folder for the first time
2. Close the app
3. Reopen and select a different project folder
4. Observe: the breadcrumb at the top still shows the original folder name from step 1

### Claude Model

None

### Is this a regression?

No, this never worked

### Last Working Version

_No response_

### Claude Code Version

2.1.260 (Claude Code)

### Platform

Anthropic API

### Operating System

Windows

### Terminal/Shell

PowerShell

### Additional Information

_No response_

Reproduce the stale breadcrumb in Claude Code Desktop by opening one project, closing the app, reopening it, and selecting another project on Windows. Trace the session-selection and breadcrumb/title-bar entry points, then add coverage for switching projects across app restarts. Done means the breadcrumb consistently shows the currently active project folder.

索引モデルが issue の本文から書いたものです。