Chrome extension not connecting to Claude Code via native messaging on Windows 11

Bug Report:

## Environment

• OS: Windows 11 Version 25H2 (Build 26200.7623)
• Claude Code version: 2.1.20 (also tested with native installer)
• Chrome version: 144.0.7559.97
• Chrome extension version: 1.0.40
• Extension ID: fcoeoabgfenejglbffodgkkbkcdhcgfn

## Issue
All mcp__claude-in-chrome__* tools return "Browser extension is not connected" despite correct configuration.

The same extension works for Claude.ai MCP connections but will not initiate native messaging for Claude Code.

## What we've verified

• Registry entry exists:

HKCU\Software\Google\Chrome\NativeMessagingHosts\com.anthropic.claude_code_browser_extension

• Native host JSON has correct extension ID in allowed_origins
• Native host batch file exists and points to valid Claude Code executable
• Extension has "Communicate with cooperating native applications" permission
• No conflicting Claude Desktop registry entries

## Troubleshooting attempted

• Killed all node/chrome processes and restarted in various orders
• Uninstalled and reinstalled Chrome extension
• Removed and recreated native host config files
• Installed Claude Code native version via claude install
• Removed conflicting Claude Desktop native host registry entry

## Key finding
When manually running the native host batch file, it attempts to CREATE a named pipe
(\\.\pipe\claude-mcp-browser-bridge-[username]) rather than connect to an existing one, causing EADDRINUSE errors
when the MCP bridge is already running.

The extension service worker shows NO activity when Claude Code attempts to use Chrome tools - it's not even
attempting to initiate native messaging.

## Expected behavior
Extension should connect to Claude Code's MCP bridge via native messaging.

## Actual behavior
Extension ignores native messaging entirely. Works for Claude.ai web MCP but not Claude Code.