I always use display capture, I personally find it better performance wise than game capture, I do game from a PC and stream on a laptop via a capture card though so I don't really need to alt tab or anything.
The problem I have with WA though, while streaming via OBS, it's just a blank screen until a game actually starts, everything in the menus says no signal found, but that doesn't bother me too much tbh I can just go to another scene in the meantime.
Of course I wouldn't complain if I knew why or could fix it but I honestly don't play WA enough to worry about it anyway.