Borderless Fullscreen, Windows 10 21H2 LTSC, HAGS enabled and GameDVR defaults (no "tweaks"). Game Bar functioning and iirc the game recognized by it. Nothing to impede the functionality. All other overlays disabled as well.
I ruled out any and all other possible software-input related problems before we found out it was Groupy2. I didn't try to group the game window. The performance issues were simply caused by Groupy being enabled for the game. If there are some kind of logs I can provide I'd gladly if possible to by anonymized.
P.S.
Sorry for another account, didn't expect a reply, this one isn't throwaway in comparison to the previous one.