claude-in-chrome MCP: Tab group lifecycle causes broken reconnection or accumulating orphaned groups

Description

The claude-in-chrome MCP extension has a tab group lifecycle issue that forces users into one of two bad outcomes:

Steps to Reproduce

Scenario A — Broken reconnection

1. Claude Code connects to Chrome via claude-in-chrome MCP, which opens a new window with a tab group
2. Close the tab inside the group
3. Chrome prompts to delete the group — confirm deletion
4. Next time Claude Code tries to connect, the extension never reconnects
5. Only fix: Uninstall and reinstall the plugin, then reconnect

Scenario B — Accumulating orphaned groups

1. Claude Code connects to Chrome, creating a new window with a tab group
2. Instead of closing the tab, close the entire window (to avoid Scenario A)
3. Next connection creates another new group in the bookmark bar
4. Over time, the bookmark bar fills with orphaned/empty tab groups

Expected Behavior

• Closing a tab or window from a previous session should not permanently break reconnection
• New sessions should reuse or clean up old groups instead of creating new ones
• There should be a clean way to end a browser session without side effects

Environment

• OS: Linux (Ubuntu)
• Claude Code: latest
• Chrome: latest stable
• Extension: claude-in-chrome (latest from MCP)