[Bug] All Claude Code sessions share single Chrome tab group instead of separate groups

Summary

When running multiple Claude Code instances in separate terminals, all browser tabs end up in the same Chrome tab group. Based on Claude Code's own documentation/behavior, each session should get its own tab group, but this isn't happening.

Current Behavior

• Start Terminal 1 with Claude Code → Creates yellow "Claude" tab group
• Start Terminal 2 with Claude Code → Tabs added to the SAME yellow group
• Start Terminal 3 with Claude Code → Still the same group

All sessions are bound to one shared tab group (confirmed via tabs_context_mcp returning the same tabGroupId across sessions).

Expected Behavior

Each Claude Code session should get its own isolated Chrome tab group, allowing:

• Independent tab management per session
• No cross-session interference
• Visual distinction between sessions

Environment

• macOS
• Claude Code version: 2.0.76
• Claude for Chrome (Beta)

Notes

• This may be an install/configuration issue on my end, or a bug in Claude Code
• Related to #15193 which also discusses multi-session tab group isolation