MCP Chrome: Extension visibly connected but Claude Code reports "not connected"

Bug Report: MCP Chrome Connection Intermittent/Broken

## Summary
Claude Code cannot communicate with the Claude Chrome extension even when the extension is visibly connected and active in Chrome.

## Environment

• Claude Code: Running (Haiku 4.5)
• Chrome Extension: Claude 1.0.50 (Installed and Enabled)
• Extension Status: Visibly connected and active in Chrome sidebar
• Account: Same account logged in both Claude Code and claude.ai

## Problem Description
The Claude Chrome extension appears connected and functional in the Chrome browser (panel visible, model selector working), but
Claude Code reports "Browser extension is not connected" when attempting to use MCP tools.

## Steps to Reproduce

1. Install Claude Chrome extension (https://claude.ai/chrome)
2. Verify extension is enabled in chrome://extensions/
3. Open Claude Code
4. Attempt to use any MCP Chrome tool (e.g., tabs_context_mcp)
5. Observe error: "Browser extension is not connected"

## Expected Behavior

• MCP tools should work when extension is visibly connected in Chrome
• Claude Code and Chrome should maintain stable communication

## Actual Behavior

• MCP tools fail with "Browser extension is not connected" error
• Extension is clearly active and functional in Chrome
• Error persists across multiple attempts
• No clear way to establish/restore communication

## Error Message
Browser extension is not connected. Please ensure the Claude browser extension is installed and running
(https://claude.ai/chrome), and that you are logged into claude.ai with the same account as Claude Code.

## Impact
CRITICAL: Unable to perform browser automation testing and debugging

## System Information

• OS: macOS
• Browser: Chrome (Latest)
• Extension Version: 1.0.50
• Claude Code: Latest