Bug: Notification badge count persists after all notifications cleared (Windows)

Description

The Copilot desktop app (Windows) shows a notification badge count on the system tray/taskbar icon even when there are no outstanding notifications, pending plan approvals, or inbox entries.

Steps to Reproduce

1. Use the Copilot desktop app normally
2. Clear/read all notifications and pending items
3. Observe the app icon still shows a numeric badge (e.g. '1' or '2')

Expected Behavior

The badge count should be 0 (no badge shown) when there are no unread notifications or pending items.

Actual Behavior

The badge persists with a stale count. It does not decrement to zero even after:

• Viewing all notifications
• Confirming inbox is empty (0 entries in session database)
• Reinstalling the app
• Clearing all caches
• App self-updating the database

Environment

• OS: Windows
• Copilot App Version: 1.0.78-2
• The issue persists across reinstalls and cache clears

Additional Context

This appears to be a state management issue where the badge count is not properly synced with the actual notification state.

No se han identificado archivos, pruebas ni puntos de entrada. Reproduce el badge obsoleto en Windows y, a continuación, sigue cómo el estado de las notificaciones y de los elementos pendientes actualiza el contador de la bandeja o de la barra de tareas; se considera terminado cuando el badge llega a cero al borrar las notificaciones y los elementos pendientes, incluso después de reinstalar y en escenarios de borrado de la caché.