Remote Control: mobile new-session model chip (Fable 5) ignored — spawned session silently runs host default (Opus)

## Summary
When spawning a new session on a Remote Control device from the Claude mobile app, the model chip in the composer showed **Fable 5**, but the session that actually spawned on the host Mac ran **Opus** (visible in the session's own model indicator, and confirmed by output quality). The chip's selection is silently ignored; the session uses the host's default model instead.

## Environment
- Claude Code 2.1.224 on macOS 26.6.2 (host), `claude rc` in spawn mode (same-dir)
- Claude iOS app, new-session composer for the paired Mac device
- Host had **no** `model` key in `~/.claude/settings.json` at the time (subscription auth, Max plan)

## Steps to reproduce
1. On a Mac with no default model configured, run `claude rc` (spawn mode: same-dir).
2. In the iOS app, open the paired device and tap New session — the composer's model chip shows "Fable 5".
3. Send a prompt and check the spawned session's model indicator.

## Expected
The spawned session runs the model shown in the composer chip (Fable 5), or the chip reflects what will actually run.

## Actual
The session runs Opus (the host-side fallback). The chip continues to display Fable 5, so the mismatch is silent — the user only notices from the session UI or from output quality.

## Workaround
Pinning `"model": "claude-fable-5"` in the host's `~/.claude/settings.json` makes spawned sessions run Fable regardless of the chip.

Start with the `claude rc` spawn-mode entry point and the host `~/.claude/settings.json` model fallback, then reproduce from the iOS new-session composer with the model chip set to Fable 5. Trace where the chip’s selection is handed to the spawned host session; done means the session runs the selected model or the chip accurately reflects the host fallback, verified in the session model indicator.

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