Chrome native host wrapper hardcodes stale Claude Code version after update

Bug Description

The Chrome native messaging host wrapper script at ~/.claude/chrome/chrome-native-host hardcodes a specific Claude Code version path, but this path is never updated when Claude Code auto-updates. This causes the Claude-in-Chrome browser automation tools to silently fail to connect.

Steps to Reproduce

1. Install Claude Code (e.g., v2.1.42) and set up Chrome integration
2. Claude Code auto-updates to a newer version (e.g., v2.1.44)
3. Try to use any mcp__claude-in-chrome__* tool
4. Get error: "Browser extension is not connected"

Root Cause

The wrapper script at ~/.claude/chrome/chrome-native-host contains a hardcoded path:

#!/bin/sh
# Chrome native host wrapper script
# Generated by Claude Code - do not edit manually
exec "/Users/<user>/.local/share/claude/versions/2.1.42" --chrome-native-host

When Claude Code updates to 2.1.44, the old 2.1.42 binary still exists on disk so there's no obvious error, but the version mismatch prevents the native host from connecting to the current extension.

Expected Behavior

Either:

• The auto-update process should regenerate ~/.claude/chrome/chrome-native-host to point to the new version
• Or the wrapper script should dynamically resolve the current version (e.g., via a current symlink or by reading a version file)

Workaround

Manually edit ~/.claude/chrome/chrome-native-host to point to the current version, then restart Chrome:

# Check current version
claude --version
# Edit the script to match
# Restart Chrome

Environment

• Claude Code: 2.1.44 (was 2.1.42 when native host was generated)
• macOS Darwin 25.1.0
• Chrome 144
• Native host config: ~/Library/Application Support/Google/Chrome/NativeMessagingHosts/com.anthropic.claude_code_browser_extension.json