Upgrade process hangs... DllHost.exe hangs the upgrade

### Microsoft PowerToys version

0.100.0

### Installation method

PowerToys auto-update

### Area(s) with issue?

Installer

### Steps to reproduce

1. Have an existing installation of PowerToys with various PowerToys running.
2. Run the setup to upgrade PowerToys.
3. Note during the setup, it will hang.

This is where things get interesting. I loaded up System Informer (think Task Manager but much more powerful) and on the Processes tab, I told it to search for anything PowerToys related and it found two instances of DllHost.exe running and sure enough, those two instances of DllHost.exe have ties to PowerToys or at least have a component of PowerToys running in its memory space.

I killed off those instances and bingo, the upgrade process continued.

### ✔️ Expected Behavior

Well, I would expect that the setup wouldn't hang up.

### ❌ Actual Behavior

_No response_

### Upload Bug Report ZIP-file

_No response_

### Additional Information

**OS Version:** Windows 11, 25H2 26200.8655
**.NET Version:** Unknown
**System Language:** English
**User or System Installation:** System
**Running as admin:** Yes

### Other Software

_No response_

Start by reproducing the PowerToys auto-update on Windows 11 with multiple PowerToys components running, then inspect the DllHost.exe processes during the hang. The issue is done when the upgrade completes without requiring those processes to be terminated manually.

Written by the indexing model from the issue text.