[BUG] Remote Control: effort label differs between host and viewing client for the same session (macOS desktop ↔ desktop)

What's Wrong?

With one Claude Code session viewed from two Macs, the two composers show different effort levels for the same running turn.

• Mac A is the host: the desktop app's Code tab, where the local session runs. Its composer shows Opus 5.5 · High.
• Mac B is the same session opened through Remote Control in the desktop app on a second Mac. Its composer shows Opus 5.5 · Extra.
• Both show the in-progress spinner for the same turn.
• The session's own metadata, read from inside the session with the session-management tool, reports model: claude-opus-5-5, effort: "high", remoteControlState: "on".

So the Remote Control client displays an effort level the session isn't using.

What Should Happen?

• Every client attached to a session shows the session's actual effort and model.
• If a client's picker holds a pending value for its next message, it should be labeled as such, not shown as the session's current state.
• Changing effort on one client should update the others, or fail visibly.

Impact

The user can't tell which effort a turn is actually running at. It's unclear whether a message sent from Mac B uses Extra or High, which affects both cost and quality.

Steps to Reproduce

1. On Mac A, start a local session in the desktop app's Code tab with effort High and turn on Remote Control.
2. On Mac B, open the same session through Remote Control in the desktop app.
3. Compare the model/effort label in both composers while a turn is running: Mac A shows High, Mac B shows Extra.

Environment

• Claude desktop app (Code tab) on macOS 26.7.x on both machines; host is a MacBook Pro.
• Model: claude-opus-5-5.
• Observed 2026-09-29.

Related

#84225 covers Remote Control model/effort/mode changes not reaching the desktop session, from mobile to Windows. This report is a desktop-to-desktop macOS case where the displayed effort differs between clients.