feat: option to disable 'Chrome extension not detected' startup notification

Summary

Every time Claude Code starts, it shows a notification banner:

Chrome extension not detected · https://claude.ai/chrome to install

There's no setting to suppress this. Even when claude-in-chrome is listed in disabledMcpServers in .claude.json, the notification still appears.

Use case

Users who use alternative browser automation tools (e.g., chrome-devtools-mcp via CDP) don't need the Claude in Chrome extension but are nagged on every startup. This is especially relevant for headless/remote setups where a Chrome extension isn't practical.

Proposal

Add a config option to disable the chrome extension detection check, e.g.:

{
  "chromeExtensionNotification": false
}

Or at minimum, respect the fact that claude-in-chrome is already in disabledMcpServers and skip the notification when the user has explicitly disabled it.

Environment

• macOS (Apple Silicon)
• Claude Code latest
• Using chrome-devtools-mcp (Google's official CDP-based MCP) as browser automation tool instead of claude-in-chrome