On KDE, kwin Window Rules will allow you to force windows onto screens, and a ton of other stuff. It’s one of the best features on Plasma that I now miss on Windows
You can just force it forever, or do “apply initially” so it just starts in a particular configuration - size, position, screen, virtual desktop, etc.








Haven’t used Mint in many many years. I searched around - try this https://cinnamon-spices.linuxmint.com/extensions/view/111 (if on Cinnamon)
For MATE, I found this https://ubuntu-mate.community/t/compiz-configuration/24928
I think there might also be some native settings options like “remember window positions” but that might be hit-or-miss