Window state save restoration must implemented by the compositor itself. Not sure about GNOME, but KDE doesn’t have that.

Actually KDE has a feature where you can set which display any app shows on, and if it should be maximized horizontally or vertically or both.

I use that for Firefox specifically, as I always like it on my secondary monitor.

Just right click on the title bar of any application to get to those settings.

(I'm using KDE on Fedora.)