That's strange; you should be able to do that with the standard xdg-shell protocol, though I suppose it depends on the app's behavior. The app can tell the compositor which output to fullscreen each window on.

Alternately, if it's using layer-shell windows, those can also be pinned to a specific output.

If it's not layer-shell, and the windows aren't fullscreen, then yes... it's annoying. The xdg-session-management protocol will likely fix that in this particular case (at the expense of having to manually place the windows in the right places once, and then it can remember in the future), but that protocol has just recently been stabilized and of course no one supports it yet.

It's all so frustrating watching the Wayland folks reinvent everything, poorly, and after more than 10 years it's still not there yet.