Is your feature request related to a problem? Please describe.
Currently, users only know if they're connected to a browser, but not how healthy that connection is, which can lead to unexpected behavior if the connection becomes unstable.

Describe the solution you'd like
Add a simple visual indicator in the status bar that shows connection health (green/yellow/red) and displays connection latency on hover.

Tasks

• Implement periodic ping to the connected browser tab
• Add visual indicator to the status bar
• Show connection latency when hovering over status item
• Handle reconnection logic for unstable connections

Technical Details

• Extend the BrowserMonitor class in src/browser/monitor.ts
• Update the status bar UI component
• Use Chrome DevTools Protocol for connection health checks