"DesktopWindowXamlSource" appears in taskbar if ("Compatibility") headless and "Startup" > "New Instance Behavior" set to ANYTHING OTHER THAN "Create new window"

### Windows Terminal version

v1.22.10731.0 (Stable)

### Windows build number

Windows 10 - Version 10.0.19045.5608

### Other Software

Microsoft PowerToys is not installed.

### Steps to reproduce

Originally a part of #18784

While enabling "Compatibility" option in the latest stable release [v1.22.10731.0], the ghost "DesktopWindowXamlSource" window does not appear in taskbar as long as "Startup --> (New Instance Behavior) is set to (Create new window)", otherwise if it set to any of the 2 other options, once WT closes, it can never be opened again until...

1. Open "Task Manager"
2. search for "Windows Terminal" in "Background Processes"
3 End it.
4. then open WT again.

Related to the ghost "DesktopWindowXamlSource" window mentioned in #18784

The "Compatibility" option allows for quick launch of WT, say an average of 0.0800s with "Compatibility" option enabled vs cold launch of 0.3100s with "Compatibility" option disabled vs "%SystemRoot%\system32\cmd.exe" launch of 0.0460s. (Calculated using PassMark AppTimer).

The "Compatibility" option is crucial for smooth experience but unfortunately it is completely fucked up in Stable, Preview & Canary releases.

Please see this [video](https://mega.nz/file/beJUBbZD#1Aqg5TjnPCDXSMnn6lLZyr-HM8Yp0LpjnbX9NwI2T24) for more clarification (The video demonstrate the "Compatibility" & "New Instance Behavior" options conflict on Portable mode only on all releases).

### Expected Behavior

"DesktopWindowXamlSource" should never be exposed.

### Actual Behavior

"DesktopWindowXamlSource" is exposed

Reproduce on Windows 10 with Compatibility enabled and each Startup > New Instance Behavior option, following the Task Manager recovery steps in the report. Read the related issue #18784 and compare the three setting combinations; done means the DesktopWindowXamlSource window is no longer exposed and Windows Terminal can be reopened normally.

Written by the indexing model from the issue text.