[FEATURE] iOS Remote Control: show "connected" confirmation after handshake

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

When connecting to a CLI session from the iOS app via /remote-control, the app shows a Remote control connecting… banner at the top during handshake, but nothing replaces it once the connection is established. There's no positive confirmation that the bridge is live — the user has to send a message and wait for a response to find out. Same gap on teardown: no explicit "disconnected" state.

Proposed Solution

After a successful handshake, replace Remote control connecting… with a brief Connected to <session-name> confirmation (could auto-dismiss after a couple seconds or persist as a subtle status indicator). On teardown, show Disconnected for symmetry.

Alternative Solutions

Workaround today: send a no-op message and watch for a reply. Works, but adds round-trip latency to every "did it actually connect?" check.

Priority

Low - Nice to have

Feature Category

Interactive mode (TUI)

(Closest fit — this is iOS app UX, but no mobile-app category exists in the template.)

Use Case Example

1. On laptop: start a session, run /remote-control brads-20260425-session-2.
2. On iOS: tap the session to connect.
3. App shows Remote control connecting… at the top.
4. Today: banner sits there indefinitely; unclear whether handshake succeeded or stalled.
5. With this feature: banner flips to Connected to brads-20260425-session-2, giving immediate confirmation the bridge is live.

Additional Context

_None._