Can't run Windows Terminal without Administrator

### Windows Terminal version

1.13.11431.0

### Windows build number

10.0.19041.572

Yes, this has actually downgraded since my last bug report. Blame the fact that I had limited download options.

### Other Software

_No response_

### Steps to reproduce

See https://github.com/microsoft/terminal/issues/13099#issuecomment-1138459416 and the comments leading up to it.

1. I was given a command that completely ruined every app on my system.
2. I had to do an in-place upgrade to fix the issue.
3. Windows Terminal, through any amount of reinstalls, now cannot run without Administrator.

### Expected Behavior

_No response_

### Actual Behavior

Windows Terminal, through any amount of reinstalls, now cannot run without Administrator. I also cannot double-click the msixbundle to install (I get some permission error), but `Add-AppxPackage` works.

The `wt` command is not found in a non-Administrator Command Prompt, but it is found in an Administrator Command Prompt.

No Start Menu entries work for any part of Windows Terminal, not even the shortcuts, *unless* run as Administrator.

Start by reviewing the linked issue and comment thread, then reproduce the installation and launch behavior using Add-AppxPackage, the wt command, and the Start Menu shortcuts. Compare Administrator and non-Administrator Command Prompt behavior. Done means Windows Terminal installs and launches normally without Administrator privileges, including the wt command and Start Menu entries.

Written by the indexing model from the issue text.