[BUG] Mods: split view draws AbovePrompt plugin bands in the left pane only

Preflight Checklist

• [x] I have searched existing issues and this hasn't been reported yet
• [x] This is a single bug report (please file separate reports for different bugs)
• [x] I am using the latest version of Claude Code

What's Wrong?

In the desktop app's Code tab, with two sessions shown side by side in split view, a mod's ui.render hook on { component: 'AbovePrompt' } draws its band in the left pane only. The right pane shows no band at all, while the app's own PR card above the prompt still shows in both panes.

It depends on the pane, not on the session:

| Probe | Observed | Rules out |
|---|---|---|
| Open the right pane's session alone (no split) | band shows | the session's own state (hook error, no data yet) |
| Both sessions in split view | band only in the left pane | — |
| Plugin enabled at user scope, no project-level override | same in both projects | plugin not enabled for one project |
| Both sessions' processes started after the same plugin version was cached | same version in both | a stale plugin copy in one session |

What Should Happen?

Each pane in split view draws its own session's AbovePrompt plugin bands, as it does when that session is opened alone.

Error Messages/Logs

None seen. The sessions were not started with --debug.

Steps to Reproduce

1. Install a mod with a ui.render hook on { component: 'AbovePrompt' } that returns a tree for the desktop surface (for example usage-band@usage-band from github.com/zexion7873/usage-band), enabled at user scope.
2. In the desktop app's Code tab, open two sessions in different projects and put them side by side (drag one from the sidebar, or Open in → Split view).
3. Let each session finish a turn so its band has data.

Expected: a band above the prompt in both panes. Actual: only the left pane has one. Opening the right session alone shows its band.

Claude Code Version

2.1.295 (the desktop app's bundled Claude Code)
Claude desktop app 2.31226.1 (857652)

Platform

macOS, Claude desktop app, Code tab