Feature: run `claude rc` as a background daemon (no open terminal, auto-restart on reboot, start/status/stop control)

Problem

Right now claude rc has to run in a terminal that I keep open for the whole time I want the remote connection alive. As soon as I close that terminal, the remote connection breaks. Worse, it breaks silently: my remote devices still show the connection as online even though it is dead (I suspect that stale "online" status is a separate bug).

This means I cannot cleanly start remote control and walk away. I have to keep a terminal window dedicated to it, and if the terminal or the machine restarts, remote control is gone until I manually start it again.

Proposal

Make claude rc able to run as a background daemon:

• Starting claude rc (or claude rc --daemon, to keep the current foreground behavior as default) spawns a background process, so I do not have to keep a terminal open.
• I can see the running daemon's status somewhere (e.g. claude rc status) and stop it when I want (e.g. claude rc stop).
• The daemon auto-restarts on machine reboot, so remote control keeps working across restarts without manual intervention.

Why this helps

• No dedicated terminal window has to stay open.
• Remote control survives terminal close and machine reboot.
• Clear lifecycle control (start / status / stop) instead of "kill the terminal."

Related

• The silent stale "online" status when the connection dies is likely a separate bug and I plan to report it separately.

Environment

• Claude Code version: 2.1.210
• OS: Linux (WSL2)