claude-in-chrome: Browser extension not connecting despite correct native messaging host setup

Bug Report

Claude Code version: 2.1.141
OS: macOS 14.6.0
Chrome extension ID: fcoeoabgfenejglbffodgkkbkcdhcgfn

## What's happening
The mcp__claude-in-chrome__tabs_context_mcp tool consistently returns "Browser extension is not connected" even though:

• Extension is installed and logged in with the correct account
• Native messaging host manifest is correctly installed at `~/Library/Application

Support/Google/Chrome/NativeMessagingHosts/com.anthropic.claude_code_browser_extension.json`

• The manifest points to the correct binary at /Users/<user>/.claude/chrome/chrome-native-host
• The binary /usr/local/lib/node_modules/@anthropic-ai/claude-code/bin/claude.exe exists and is executable

## Additional context
claude mcp list only shows Supabase and Playwright — claude-in-chrome does not appear in the list at all.

There are two native messaging host manifests registered for the same extension ID:

• com.anthropic.claude_browser_extension → Claude Desktop app
• com.anthropic.claude_code_browser_extension → Claude Code

Both list the same extension ID (fcoeoabgfenejglbffodgkkbkcdhcgfn) in allowed_origins. Possible conflict.

## Steps tried

• Restarted Chrome
• Verified logged into claude.ai with same account
• Quit Claude Desktop app
• Verified extension is enabled in chrome://extensions