[BUG] Claude in Chrome: Tab groups don't persist, connection drops during long tasks

What's Wrong?

Claude in Chrome's MCP tab group handling has three related issues that severely impact long-running workflows (server administration, multi-step deployments, debugging):

1. Tab groups don't persist across sessions. Each new Claude session creates a new "Claude (MCP)" tab group instead of reusing an existing one. Old tab groups accumulate and need manual cleanup. If the user prepares tabs in advance (logged into services, navigated to the right pages), Claude can't see them because they belong to a previous session's tab group.

1. Connection drops during inactivity. The Chrome extension's service worker goes idle during extended operations (e.g., waiting 15-30s for a terminal command to complete). This severs the connection entirely, requiring reconnection and often losing context about which tabs were in use.

1. No manual connect/disconnect control. There's no way for the user to explicitly manage the connection lifecycle. Disconnections happen silently and unpredictably.

Expected Behavior

• One persistent tab group called "Claude (MCP)" that survives across sessions. If the user prepares tabs (logs into services, opens relevant pages), the next Claude session should see and use those tabs.
• Longer idle timeout or a keepalive mechanism so the connection doesn't drop during normal agentic workflows.
• Explicit Connect/Disconnect button in the extension UI so users can manually control the connection state.

Why This Matters

Many real-world tasks require the user to pre-authenticate into services (VPS terminals, admin dashboards, internal tools) before Claude can work. Users may not want to hand credentials to Claude or watch it fumble through login UIs, which burns tokens, wastes time, and creates security concerns. The current model of "Claude opens everything fresh each session" doesn't work for these workflows.

Long-running agentic tasks routinely involve commands or waits that exceed the service worker's idle timeout. Having the connection drop mid-task forces repeated reconnection, context loss, and wasted effort. In a recent 3-session server administration workflow, the connection dropped 5+ times.

Steps to Reproduce

1. Open Chrome, create a tab group with tabs logged into various services
2. Start a Claude Desktop / Cowork session that uses Claude in Chrome
3. Claude creates a NEW tab group instead of reusing the prepared one
4. During the session, run any operation that takes >15 seconds (e.g., a terminal command with sleep)
5. Connection drops, requiring reconnection

Claude Code Version

Latest (Cowork mode, Claude Desktop macOS)

OS

macOS

Checklist

• [x] I have searched existing issues and this hasn't been reported yet
• [x] This is a single bug report
• [x] I am using the latest version of Claude Code