Mobile app hides remote-control sessions until Claude GitHub App is installed; web banner stale after install

**What's wrong:**
With GitHub connected but the Claude GitHub App not installed, the Claude mobile app (Android) opened the Code tab straight into a "Select repository" flow and did not surface my connected remote-control sessions from the desktop app. Those sessions are local folders and don't need a GitHub repo.

After installing the GitHub App (All repositories, personal account) via "Install on GitHub" at claude.ai/code and reloading, the "Two steps to work in your repository" banner still showed step 2 unchecked, even though the repo picker listed my repos and github.com showed the app installed.

After a force-stop and restart, the mobile app now shows the remote-control sessions.

**Expected:**
Remote-control sessions should be visible regardless of GitHub App install state. The web banner should update once the app is installed.

**Environment:** Android, Claude app version [FILL IN], personal-account repos, remote control started from the Claude desktop app.

**Related:** #44805, #31401, #42006

Reproduce on Android with GitHub connected, the GitHub App absent, and a remote-control session started from the desktop app; then install the app through claude.ai/code and reload. Investigate the Code tab's session visibility and the web banner's installation state, using related issues #44805, #31401, and #42006 for context. Done means sessions remain visible without the app and the banner marks installation complete after refresh or restart.

Written by the indexing model from the issue text.