Yes, but why do I have to use a different key combination for moving windows between screens than for moving them within the screen? Besides, this moves the window to the same position on the other screen, as it currently is on the current screen.

It would be much more useful, and indeed the default in Windows and the several macOS implementations, to move the Window to the "next available tiling position" in the indicated direction. Thus, consecutive Win-Right should move the window to

- the right half of the left screen - the left half of the right screen - the right half of the right screen

In Gnome 3, I think the workspaces are arranged vertically by default. Win+Right makes me think of the workspace to the right, but the next workspace would be below.