Terminal env vars (`WT_SESSION`, etc) aren't set when set as the Default Terminal

[StartAutomating]

Windows Terminal version

1.12.10983.0

Windows build number

10.0.22000.0

Other Software

No response

Steps to reproduce

Change settings to launch terminal instead of command shell.
Close instances of terminal
Run powershell/pwsh
Check $env:WT_PROFILE_ID
See that it is blank

Expected Behavior

$ENV:WT_PROFILE_ID should never be blank, because having a blank profile ID disables changing settings for that profile.

Actual Behavior

$ENV:WT_PROFILE_ID is not set when terminal is launched with pwsh/powershell, after changing system settings.