Model picker state diverges between desktop and mobile clients on a remote-controlled code session

Description

When a Claude Code session (desktop app, agent/code session) is remote-controlled from the mobile app, the model picker shows different selected models on each client for the same session. Each client appears to display its locally-set model rather than the session's authoritative state.

Steps to reproduce

1. Start a code session in the macOS desktop app with remote control enabled.
2. On desktop, run /model haiku → desktop footer shows Haiku 4.5.
3. On the mobile app attached to the same session, open Change model and select Fable 5.
4. Compare the two clients.

Expected

Both clients show the same (authoritative) model for the session, and a model change from either client syncs to the other.

Actual

• Mobile app: model picker shows Fable 5 selected (checkmark).
• Desktop app: footer for the same session still shows Haiku 4.5.
• No sync occurs in either direction; it's unclear to the user which model is actually serving the session.

Screenshots of both clients (taken seconds apart on the same session) attached in the comment below / can be provided.

Environment

• macOS (Darwin 25.0.0)
• Claude desktop app 1.12603.1
• Claude Code runtime 2.1.170
• Session started on desktop, remote-controlled from iOS app
• Models involved: Haiku 4.5 (set via /model on desktop), Fable 5 (set via mobile picker)

Additional context

The assistant inside the session also cannot reliably report the active model: the environment info in its system prompt is written at session launch and goes stale after runtime model switches, so there is no in-session way to confirm which model is actually in effect.