[Bug] Windows Desktop: Multiple project sessions share same CLI instance and closing one affects others

Description

When running multiple Claude Code sessions for different projects via the Desktop app on Windows, two problems occur:

1. CLI navigation merges: Clicking "Navigate to CLI" initially works correctly per project, but after a few minutes, all projects' buttons redirect to a single CLI instance instead of their respective ones.
2. Closing one session affects others: Closing one project's session via the close button appears to impact other running sessions (possibly related to shared session/process management).

Steps to Reproduce

1. Open Claude Code Desktop app on Windows
2. Start multiple sessions for different projects using the run button
3. Initially, clicking "Navigate to CLI" correctly switches to each project's CLI
4. Wait a few minutes
5. Click "Navigate to CLI" on any project → all of them now navigate to the same single CLI instance
6. Close one session → other sessions may be affected

Expected Behavior

• Each project should maintain its own independent CLI instance at all times
• Closing one session should not affect other running sessions

Environment

• OS: Windows 11 Pro 10.0.26200
• Claude Code Desktop app

Related Issues

• #42536 (multiple sessions collide on temp dir)
• #41342 (closing terminal tab does not close Claude)
• #30154 (multi-window support request)