Definitely. You can set tiling shortcuts in system settings. Personally, I use my numpad so that e.g. meta + num7 tiles to the top-left. You can also move windows from monitor to monitor that way.
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.
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.
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.