Linux

Seems like this is possible, but the method (and maybe ability) depends on your window manager.

If you're using x11, you can interact with the window manager via the command line (so could set up the whole thing in a script). An example command line tool: xdotool (search for "interacting with x11 via command line" for more info).

If you're on Wayland, one of the design principles was to avoid programmatically interacting with window size or position; the user will set up their composer to behave as they want, not how the programmer of that program wants, and especially not how programmers of other arbitrary programs want (it was a security issue at the extremes, or could be annoying for more common cases). But you, the user, do have control, though it depends on your DE and what Wayland compositor it is using. On fedora KDE, you can use KWin scripts (which supports several languages).

There's also some other window managers that can offer better control, and perhaps it's enough for the window manager to simply remember the position of windows when they are closed (which I think Wayland does or can be configured to do easier than writing a script, then you just need a launch script for the programs in your shortcuts).