[BUG] Remote Control (mobile): backgrounding the app resets a running session's model to Opus 4.8

### Environment
- Claude mobile app (iOS)
- Host: Claude desktop app 1.52386.6 on macOS 26.6.2 (Mac17,9), Claude Code CLI 2.1.266

### What happens
A model chosen for an existing session in the mobile app does not survive backgrounding. Background the app, reopen it, and the session's model indicator reads **Opus 4.8** again. Reproduced repeatedly across several sessions on 2026-09-14; the reset happens every time, not intermittently. The same reset behaviour has since been observed on the desktop app as well.

### Steps to reproduce
1. In the mobile app, open an existing session and select a model other than Opus 4.8.
2. Background the app.
3. Reopen it and check the model indicator.

### Expected
The per-session model selection persists across app lifecycle transitions until it is changed.

### Why this is not a duplicate of the nearby reports
The trigger is different from the other "model went back to Opus" issues:
- #89358 — a pinned model overridden mid-session by a conservative switch (Linux).
- #90670 — the new-session model chip ignored at spawn time, so the spawned session starts on the host default.

Here the session is already running, the model was chosen explicitly for it, no turn is in flight, and the only event between the correct state and the wrong one is the app going to background and coming back.

### What I cannot provide
No instrumented evidence. The session record stores a single `model` field and I did not sample it before and after backgrounding, so this is filed on repeated user-visible reproduction rather than captured state. Happy to collect before/after samples of the session record if that would help triage.

🤖 Generated with [Claude Code](https://claude.com/claude-code)

The report names no source files, tests, or entry points. Start by locating the remote-control session lifecycle and the code that persists and restores a session's selected model, then reproduce the background-and-reopen sequence on mobile or desktop. Done means an explicitly selected model remains unchanged across the app lifecycle transition.

Written by the indexing model from the issue text.