Remote Control: allow choosing which paired Mac to start a new Code session on

Problem
When starting a new session from the mobile app's Code tab (tap "+ New Session"), it always targets one fixed default local Mac, with no picker to choose among multiple paired Macs. If that default Mac is offline, session creation just fails with a generic network error, with no way to pick another paired Mac instead.

Repro

1. Pair Remote Control on two different Macs (e.g. after migrating to a new Mac while keeping the old one around).
2. From the mobile app's Code tab, tap "+ New Session".
3. The new session always targets the same device (seemingly whichever was paired/registered first), even when that Mac is offline.

Expected
A device picker when starting a new session, so any currently paired/online local Mac can be chosen.

Workaround found
Starting claude locally on the desired Mac makes that session appear (as connected) in the mobile Code tab's session list. But there's no way to initiate a brand-new session targeting a specific machine from the mobile app itself — only existing/already-started sessions are selectable.

Possible cause
This may be related to a stale "default device" registration that carried over after migrating to a new Mac via Migration Assistant — the old Mac's identity/local config appears to have been copied over, and it still seems to be treated as the default target for new sessions even though the new Mac is the one actually in use.