Always on Top appear on title bar context menu only on enabling it with shortcut the first time and as well as on reopening application

### Microsoft PowerToys version

0.98.0

### Installation method

PowerToys auto-update

### Area(s) with issue?

Always on Top

### Steps to reproduce

- Toggle the option to add `Always on Top` on title bar's context menu in PowerToys
- Open any supported application right-click on title bar -> Always on Top won't be there.
- Use shorctcut `ctrl + win + T` the first time you open the application and then till you close it, you will have access to Always on Top option to both enable and disable in title bar context menu.
- When you reopen the application, it's won't be there again, we need to use shortcut then it will be there till we keep the app open.

### ✔️ Expected Behavior

- Toggle the option to add `Always on Top` on title bar's context menu in PowerToys.
- When we open any supported app, we should be getting `Always on Top` option in title bar's context menu by default.

### ❌ Actual Behavior

- Toggle the option to add `Always on Top` on title bar's context menu in PowerToys.
- When we open any supported app, `Always on Top` option in title bar's context menu is only appearing on using the shortcut first time, and also on using shortcut after reopening the application

### Upload Bug Report ZIP-file

[Screenshot 2026-03-18 121627.png](https://github.com/user-attachments/assets/fecbce55-bf33-4dbe-95f2-f7be9d7f9654)
[Screenshot 2026-03-18 121700.png](https://github.com/user-attachments/assets/3ca0f830-f96d-4072-ac61-c9fec85404c2)
[Screenshot 2026-03-18 121825.png](https://github.com/user-attachments/assets/90cf4482-eb6d-4db2-9ef8-cf7ed3a1bd04)
[Screenshot 2026-03-18 121852.png](https://github.com/user-attachments/assets/b118c8ba-5813-4e3d-a499-b02b87b87d1a)

### Additional Information

OS Version: 25H2
PowerToys version: 0.98.0

### Other Software

_No response_

Begin by reproducing the Always on Top title-bar context-menu behavior using the listed toggle, shortcut, and application-reopen steps. Trace the Always on Top context-menu integration and verify that enabling the setting makes the menu item available immediately when supported applications open and after reopening them.

Written by the indexing model from the issue text.