Remote control: web panel resets a session's effort to account-last-used (Medium), overriding the project effortLevel pin

Environment

• Claude Code v2.1.212 on Linux (headless Hetzner server)
• Sessions started via the remote-control bridge (entrypoint: claude-vscode), driven from the claude.ai/code web UI
• Two concurrent sessions under one account on the same machine:
• Session A: cwd ~/boxen/real-tavern-dispatch, project .claude/settings.local.json pins "model": "claude-fable-5[1m]", "effortLevel": "xhigh"
• Session B: cwd ~, user-global ~/.claude/settings.json has "model": "claude-fable-5[1m]", "effortLevel": "high"; the panel shows Fable · Medium

Steps to reproduce

1. Session A is pinned to Fable · x-high via project settings.local.json and confirmed with /effort xhigh in that panel.
2. Interact with Session B's panel, which shows Fable · Medium.
3. Return to Session A's panel: its model/effort selector shows Medium again. This repeats every time after using the other panel.

Expected

Each remote-control panel reflects (and preserves) its own session's effort level.

Observed

The picker appears account-sticky — the last-used selection from one panel bleeds into the other panel's session.

Evidence this is the web layer, not the CLI or settings files

• "medium" appears nowhere on the machine: user-global effortLevel is high, the project pin is xhigh, and Session A's transcript records no incoming medium-effort change.
• Fable 5's documented default effort is high, so Medium is not a CLI-side fallback.
• We cannot determine whether this is display-only or an actual session override, because bare /effort produces no output in the remote-control web UI (filed separately) — there is no way to read the session's actual effort to check.

Possibly related (settings-file-level effort leaks, which this is not, since no file here ever contains "medium"): #49076, #49166.