PowerShell argument `WindowStyle -Hidden` is not respected when the default terminal application is Windows Terminal

### Windows Terminal version

1.12.10393.0

### Windows build number

Microsoft Windows NT 10.0.22549.0

### Other Software

|Software | Version|
|---| --- |
| PowerShell.exe | Multiple Versions |
| pwsh.exe | Multiple Versions |

### Steps to reproduce

1. Set Windows Terminal as the default terminal application:
.

2. Make sure to save changes to Windows Terminal Settings, and then using Windows Run, run `pwsh -WindowStyle Hidden -Command Sleep 10`:

### Expected Behavior

A new PowerShell process launches (Windows Terminal), and it isn't visible. The window _may_ flash for a second. PowerShell window shouldn't be displayed when it's launched with `WindowStyle -Hidden`.

### Actual Behavior

A new PowerShell process launches (on Windows Terminal), and it is visible and remains visible (and waits) for 10 seconds.


Note: There is no repro for this issue with `Windows Console Host` as the default terminal application.

Reproduce the behavior with Windows Terminal set as the default terminal and run `pwsh -WindowStyle Hidden -Command Sleep 10`, comparing it with Windows Console Host. Trace the Windows Terminal handling of PowerShell process launch and window visibility; done means the hidden launch remains invisible while the existing console-host behavior is preserved.

Written by the indexing model from the issue text.