[Feature]: MCP Bridge Extension - More easily visually identify active tabs

[mrw]

Motivation

When using Playwright's MCP Bridge in Chrome, it's not always easy to tell which window is actually "owned by" and being controlled by Playwright. Claude Cowork solves this by putting its controlled tab in a colored tab group so you can quickly tell which tab is automated. I propose that the Playwright MCP Bridge does the same.

I've already created a PR, #1422, for consideration of this improvement and to show its implementation.

Proposed behavior

1. Orange tab group — When the extension connects to a tab, place it in an orange-colored tab group titled "Playwright MCP" using chrome.tabs.group() / chrome.tabGroups.update().
2. New window — If the controlled tab shares a window with other tabs, move it to a new window via chrome.windows.create({ tabId }). (This part is less critical than point 1 i think).
3. Cleanup — On disconnect (or tab close), ungroup the tab. The now-empty group auto-deletes.

Implementation notes

• Adds the tabGroups permission to manifest.json, shown here.
• Changes are all inpackages/extension/src/background.ts (tab group + window logic in _connectTab, cleanup is in _setConnectedTabId / _onTabRemoved).
• I also added tests for this behavior.

Thank you for your consideration!