Copilot window can become stuck always on top until app restart

### Description

The GitHub Copilot App somehow entered a persistent topmost window state on Windows. After that happened, the main Copilot window remained in front of every other application when I switched focus, covering those apps.

There was no visible always-on-top or pin control in the title bar or app UI, and I do not have PowerToys installed, so this was not caused by PowerToys' Always On Top feature.

### Reproduction

I do not yet know what action triggered the state. The app had been used normally across multiple sessions and eventually began behaving as an always-on-top window.

### Actual behavior

The Copilot window stayed above all other application windows even after another app received focus.

### Expected behavior

Unless explicitly requested by the user, the Copilot window should follow normal Windows z-order and move behind the active application.

### Workaround

Fully restarting the GitHub Copilot App cleared the topmost state and restored normal window behavior.

### Environment

- GitHub Copilot App: 1.1.10
- Windows: 10.0.26200.0
- PowerToys: not installed

まず、報告された app と OS のバージョンを使って、Windows 上で永続的に always-on-top になる挙動を再現し、その後 desktop のウィンドウ状態処理を調査します。どの操作またはライフサイクルによってウィンドウが topmost のままになるのかを確認し、通常のフォーカス変更によって、app を再起動しなくても標準の z-order に戻ることを検証します。

索引モデルが issue の本文から書いたものです。