If you're on X11, you should be able to use xdotool, which doesn't depend on KDE doing anything in particular. No idea what the equivalent is if you're on Wayland.

xdotool can move a window?

Yes! See the windowmove command!

You can do Alt+F3 ↓ ↓ ↓ → enter and then move the window using cursors keys (and hit enter to apply the window position)

You can also assign a shortcut to get to this point (in Shortcuts -> Global Shortcuts -> System Settings -> Move Window).

I don't think you can get what you're asking for without writing a tiny script and setting it to be invoked with your keyboard shortcut.

While it works, the problem with "Alt+F3 ↓ ↓ ↓ →" is that when I move the window afterwards, the cursor keys get passed through to the window. So when I do that on Firefox, the website scrolls up and down. When I do it on a terminal, it invokes my bash history.

Try the arrow key(s) (after selecting resize in window menu) while pressing down Super key.

Which one is the "Super Key"? If it is the window key - that one in combination with the arrows is already mapped to tiling functions. Window+UP makes the current window take half of the screen on the upper side.

Oh sorry, use shift key + arrow keys. Not the super key.