Auto Dark Mode stops Spotlight changing wallpaper

### Description

After installing Auto Dark mode, windows spotlight no longer downloads new wallpapers. It only switches between the 4 wallpapers it already has. Uninstalling ADM fixes this

### Expected Behavior

_No response_

### Log Data

attached

### Commit Hash, Version and Windows Build

- Commit: `5678573e`
- Service/App: `11.0.0.54`
- Updater: `4.0.3`
- Shell: `1.3.3.0`
- .Net: `9.0.8`
- Windows: `26200.8328`
- Arch: `X64`

[service.log](https://github.com/user-attachments/files/27391765/service.log)

### Screenshots / Videos

_No response_

Start by reviewing the attached service.log and reproducing the interaction between Auto Dark Mode 11.0.0.54 and Windows Spotlight on Windows build 26200.8328. Trace the wallpaper-related service behavior and compare it with the uninstalling-ADM case; done means Spotlight downloads new wallpapers while Auto Dark Mode remains installed.

Written by the indexing model from the issue text.