Claude in Chrome MCP process doesn't reconnect when Chrome/extension restarts

Description

The --claude-in-chrome-mcp process fails to reconnect to the Chrome native host socket when Chrome or the extension restarts. The /chrome command shows "Status: Enabled" and "Extension: Installed", but all mcp__claude-in-chrome__* tool calls return "Browser extension is not connected."

Steps to Reproduce

1. Start Claude Code with claude --chrome
2. Verify Chrome extension is working (tools work)
3. Restart Chrome, or the extension disconnects for any reason
4. The native host creates a new socket (e.g., /tmp/claude-mcp-browser-bridge-main/<new-pid>.sock)
5. Try using any mcp__claude-in-chrome__* tool
6. Tool fails with "Browser extension is not connected"

Root Cause Analysis

The MCP process (--claude-in-chrome-mcp) is started when Claude Code launches but never reconnects when the socket changes.

Evidence from debugging:

=== MCP process (started 9:36PM) ===
PID 25391: /Users/main/.local/share/claude/versions/2.1.19 --claude-in-chrome-mcp

=== Native host (started 9:39PM after Chrome restart) ===
PID 25821: /Applications/Claude.app/Contents/Helpers/chrome-native-host

=== Socket ===
/tmp/claude-mcp-browser-bridge-main/25821.sock (created 9:39PM)

=== Socket connections ===
ONLY the native host (25821) is connected to the socket.
The MCP process (25391) has NO socket connections.

From chrome-native-host.log:

• Socket is created and listening: ✓
• "MCP client connected" message: Never appears

From lsof -p <mcp-pid>:

• Only has stdin/stdout/stderr (fds 0-2)
• No connection to any socket in /tmp/claude-mcp-browser-bridge-main/

Expected Behavior

1. The MCP process should poll/watch for new sockets in /tmp/claude-mcp-browser-bridge-main/
2. OR "Reconnect extension" from /chrome menu should trigger reconnection
3. OR the MCP process should restart when Chrome reconnects

Actual Behavior

• MCP process sits idle with no socket connections
• "Reconnect extension" has no effect
• Only workaround is to completely restart Claude Code

Environment

• Claude Code version: 2.1.19
• macOS (Darwin 25.3.0)
• Chrome extension installed and enabled
• Native host working correctly (creates socket, logs show it listening)

Workaround

Exit Claude Code entirely and restart with claude --chrome. This creates a fresh MCP process that connects to the existing socket.