Command Palette doesn't store results ordering.

Nobody has claimed this yet.

### Microsoft PowerToys version

0.100.0

### Installation method

WinGet, PowerToys auto-update

### Area(s) with issue?

Command Palette

### Steps to reproduce

* Type in a regular program/application search in CP.
* Select any result besides the 1st one.
* Press enter to open the app.
* Close the app.
* Call CP again and type the same input in.
* The app will be the top result or, at least, closer to the top.
* Close and reopen PT.
* Call CP again and type the same input in.
* The app's position will be reset.

### ✔️ Expected Behavior

CP should retain ordering of search results between sessions.

### ❌ Actual Behavior

Ordering isn't kept.
I've experienced this with updates and machine reboots, so far.

### Upload Bug Report ZIP-file

[PowerToysReport_2026-06-23-19-32-53.zip](https://github.com/user-attachments/files/29270075/PowerToysReport_2026-06-23-19-32-53.zip)

### Additional Information

* Microsoft Windows 10 IoT Enterprise LTSC (x64) Build 19044.7417 (21H2)
* Currently installed "classic" .NET Versions in the system:
2.0.50727.4927 Service Pack 2
3.0.30729.4926 Service Pack 2
3.5.30729.4926 Service Pack 1
4.0.0.0
4.8.04084
* en-UK
* Machine-level installation.
* Run as admin.

### Other Software

N/A

Start by reproducing the ordering behavior in Command Palette using the listed search, selection, close, and restart steps. Trace how Command Palette records result ordering and whether that state is restored after PowerToys restarts; done means the selected application retains its ordering across sessions.

Written by the indexing model from the issue text.