feat: remote control auto-reconnect and connection health status

Preflight Checklist

• [x] I have searched existing requests and this feature hasn't been requested yet
• [x] This is a single feature request (not multiple features)

Problem Statement

Problem: Remote control connection gets stuck in “Connecting” state. Only recovery is manual disconnect + restart, which requires physical access to the local machine — defeating the purpose of remote access.

Proposed Solution

Requested improvements:

1. Auto-reconnect — automatically re-establish the connection instead of staying stuck
2. Connection health status — expose state programmatically (Connected/Connecting/Disconnected/Processing) via a command, status file, or hook
3. Status during long operations — show indicator when CLI is busy (e.g., compaction) so remote users can distinguish “busy” from “disconnected”
4. Hook for state changes — enable custom recovery logic via hooks or /loop