I did have a peak at the info collected here and afaik, it didn't give me any direct clue to what is going on... but..
I did enable minimal logging (L1) and filtered out what is happening there and i maybe have found something relevant:
2024/04/03 19:02:03.7837##_##WARN:L1##_##displayfusion.exe:1096##_##TaskbarManager:ProcessTaskbarsCallbackTASKBARMANAGERTHREADONLY:933##_##-##_##Processing TaskbarButtonInvalidate from Queue: 0x00051b8e, Class: 'CASCADIA_HOSTING_WINDOW_CLASS', RectNormal: X=148, Y=156, W=1009, H=605, Style: 0x14cf0000, StyleEx: 0x00200100, Min: False, Max: False, VisSimp: True, PID: 6256, Path: 'C:\Program Files\WindowsApps\Microsoft.WindowsTerminal_1.19.10573.0_x64__8wekyb3d8bbwe\WindowsTerminal.exe'##_##-
2024/04/03 19:02:03.7879##_##INFO:L1##_##displayfusion.exe:1096##_##TaskbarEnumItemUpdate:DoButtonUpdateTHREAD:54##_##-##_##Reason: TaskbarManager:TaskbarItemSetFlash:ReloadIconAndText, Image: True, Window: 0x00051b8e, Class: 'CASCADIA_HOSTING_WINDOW_CLASS', RectNormal: X=148, Y=156, W=1009, H=605, Style: 0x14cf0000, StyleEx: 0x00200100, Min: False, Max: False, VisSimp: True, PID: 6256, Path: 'C:\Program Files\WindowsApps\Microsoft.WindowsTerminal_1.19.10573.0_x64__8wekyb3d8bbwe\WindowsTerminal.exe'##_##-
2024/04/03 19:02:03.7879##_##INFO:L1##_##displayfusion.exe:1096##_##BFImage.UniversalApps:GetIconFromUniversalAppFile:61##_##-##_##GetFromCache [UniversalApp:Manifest: C:\Program Files\WindowsApps\Microsoft.WindowsTerminal_1.19.10573.0_x64__8wekyb3d8bbwe\WindowsTerminal.exe]: C:\Program Files\WindowsApps\Microsoft.WindowsTerminal_1.19.10573.0_x64__8wekyb3d8bbwe\WindowsTerminal.exe::App::32::Dark##_##-
2024/04/03 19:02:03.9834##_##WARN:L1##_##displayfusion.exe:1096##_##WindowLocationManager:AddItem:468##_##-##_##Window Already Added: 0x00051b8e, Class: 'CASCADIA_HOSTING_WINDOW_CLASS', RectNormal: X=148, Y=156, W=1009, H=605, Style: 0x14cf0000, StyleEx: 0x00200100, Min: False, Max: False, VisSimp: True, PID: 6256, Path: 'C:\Program Files\WindowsApps\Microsoft.WindowsTerminal_1.19.10573.0_x64__8wekyb3d8bbwe\WindowsTerminal.exe'##_##-
2024/04/03 19:02:04.5317##_##INFO:L1##_##displayfusion.exe:1096##_##BFNativeHelpers:RegisterWindowMessageWrapper:188##_##-##_##Message: WMBFS_WindowCreatedReadyForAsync, ID: 49813##_##-
I'm not sure how many of those lines that are relevant, just in case...
edit: I tried to re-add the pinned app again with the same parametes and now it just instantly closes without doing anything.