Mobile UI shows wrong repo name for remote-control sessions with private repos

Description

When using claude remote-control from a generic terminal (not Claude's native terminal) inside a private repository, the mobile app (iOS/Android) displays the wrong repository name in the session header.

Steps to Reproduce

1. Open a regular terminal (not Claude's native terminal)
2. Navigate to a private GitHub repository directory (e.g., ~/leonobitech/backend)
3. Run claude remote-control
4. The environment is created with a 32-session pool (1/32, 2/32, etc.)
5. Open the Claude mobile app and navigate to the session

Expected Behavior

The session header subtitle should either:

• Display "Remote control" (like it does when using Claude's native terminal), or
• Display the actual repository path/name

Actual Behavior

The session header subtitle displays the last repository selected from the Cloud environment instead of the actual repo or "Remote control".

This happens because private repos are not available in the Cloud environment (which only shows public repos via GitHub OAuth), so the mobile UI cannot resolve the repo name and falls back to the last cloud-selected repo — showing incorrect/misleading information.

Context

• Claude's native terminal handles this correctly: it shows "Remote control" as the subtitle without attempting to resolve a repo name.
• Cloud environment only lists public repos (private repos don't appear), which is likely why the fallback occurs.
• The bug is purely cosmetic/UI — the actual session works correctly in the right directory.

Environment

• Claude Code CLI (latest)
• Claude mobile app (Android)
• macOS (Darwin 25.3.0)