Windows terminal doesn't start when using "Run as administrator"

### Windows Terminal version

1.23.12811.0

### Windows build number

10.0.26200.0

### Other Software

### Steps to reproduce

Launch Windows Terminal as administrator from the start menu using the context menu "Run as administrator" command. Or, from Windows Terminal, Ctrl+Click on new Powershell tab.

### Expected Behavior

Terminal should open the elevated command prompt.

### Actual Behavior

I see the rotating cricle next to the mouse arrow but Windows Terminal (with the elevated prompt) doesn't start. I get the UAC prompt. I click 'Yes'. And then nothing happens.

I'm running Windows Terminal on an admin account.

**I've tried the following...**

1. Uninstall/Reinstall from MS Store
2. Uninstall/Reinstall from GitHub packages

The interesting part is, after I uninstall/reinstall, the first time that I start Windows Terminal, I can run the elevated command prompts. But once I shut down the program and open it again, it doesn't work. (The behaviour then is as described in the first two paragraphs above.)

I've checked the CrashDumps folder in %localdata% but I don't see any Windows Terminal related dumps in there.

Reproduce the failure by launching Windows Terminal from the Start menu with “Run as administrator” and by Ctrl+Clicking a new PowerShell tab, then compare the first launch after reinstall with later launches. Inspect the elevated-start path around the UAC prompt and the reported absence of crash dumps. Done means an elevated command prompt reliably opens after relaunching Terminal.

Written by the indexing model from the issue text.