[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.

Written by the indexing model from the issue text.