remote-control: allow reconnecting to existing session instead of creating new one

Problem

When a /remote-control WebSocket connection drops (Mac sleep, network interruption, idle timeout), there is no way to reconnect to the existing session. Running /remote-control again creates a new session pairing, which:

1. Creates a new session in the Claude mobile/web app
2. Shows the previous session as disconnected/archived
3. Requires manually renaming each new session for identification
4. Loses the continuity of the original session in the app UI

Use Case

Running multiple long-lived Claude Code sessions (e.g., specialized agents for different tasks) connected via remote-control. When any connection drops, re-establishing requires creating new sessions for each agent — significant friction when managing 5+ concurrent sessions.

Expected Behavior

/remote-control should detect if the current CLI session was previously paired and attempt to reconnect using the same session ID, preserving continuity in the mobile/web app.

Current Behavior

/remote-control always creates a new pairing with a new session ID. No reconnect capability exists.

Workaround

Preventing drops via caffeinate and stable network — but drops are inevitable over multi-day sessions.