Dock: Killing extension process breaks dock UI interactions

### Microsoft PowerToys version

0.98

### Installation method

PowerToys auto-update

### Area(s) with issue?

Command Palette

### Steps to reproduce

1. Add Media controls to the dock
2. Play your favorite song
3. Kill the Media controls process
4. Right-click on empty space on the Dock
- Observe that Edit Dock does nothing
- Observe that Settings does nothing

### ✔️ Expected Behavior

_No response_

### ❌ Actual Behavior

_No response_

### Upload Bug Report ZIP-file

_No response_

### Additional Information

_No response_

### Other Software

_No response_

Start by reproducing the Dock issue with Media controls added, then terminate the Media controls process and test the Dock context menu. Trace the Dock handling for the process-termination case and verify that Edit Dock and Settings still respond after the extension exits.

Written by the indexing model from the issue text.