Windows Terminal cannot be launched and cannot be uninstalled/repaired

### Windows Terminal version

1.16.10262.0

### Windows build number

10.0.22621.0

### Other Software

_No response_

### Steps to reproduce

I hit close while running SQL Server in the Terminal (it is a custom build as I am on the SQL team) and it seems to have catastrophically corrupted Windows Terminal somehow to such a degree that it can't even be uninstalled.

### Expected Behavior

I should be able to launch and uninstall.

### Actual Behavior

Whenever it crashes, the following error is being reported in Event Viewer:

```
Faulting application name: WindowsTerminal.exe, version: 1.16.2301.26002, time stamp: 0x63d332f5
Faulting module name: Microsoft.Terminal.Settings.Model.dll, version: 1.16.2301.26002, time stamp: 0x63d3317c
Exception code: 0xc0000005
Fault offset: 0x00000000000fa96d
Faulting process id: 0x0x4D48
Faulting application start time: 0x0x1D97886AD310BBC
Faulting application path: C:\Program Files\WindowsApps\Microsoft.WindowsTerminal_1.16.10262.0_x64__8wekyb3d8bbwe\WindowsTerminal.exe
Faulting module path: C:\Program Files\WindowsApps\Microsoft.WindowsTerminal_1.16.10262.0_x64__8wekyb3d8bbwe\Microsoft.Terminal.Settings.Model.dll
Report Id: 5e9724bf-5d0a-452f-983a-dc42cc63b894
Faulting package full name: Microsoft.WindowsTerminal_1.16.10262.0_x64__8wekyb3d8bbwe
Faulting package-relative application ID: App
```

When I attempt to uninstall, I get error 0x80073cfa from Windows Settings.

No source files or tests are named. Start by reviewing the reported crash in Microsoft.Terminal.Settings.Model.dll and the 0x80073cfa uninstall failure, then reproduce the launch and uninstall/repair behavior on the stated Windows and Terminal versions. Done means identifying and fixing the cause so Terminal can launch and be uninstalled or repaired.

Written by the indexing model from the issue text.