Lots of weird misinformation in the comments here. Wayland doesn't choose anything. It leaves the compositor to decide where to position a window and whether or not that window receives key presses or not. The program can't draw wherever it wants or receive system wide keystrokes or on behalf of another program. When appropriately implemented the screenshot system is built directly into the compositor. It's an API that let's a program request read access to a part of the screen and the compositor provides upon approval. It's much more secure that way and it works perfectly fine these days. Unfortunately not every compositor implements this.

However if you really really really wanna side step this you can look at keyd - https://github.com/rvaiya/keyd

A project that has a daemon run in the background as a root service and that can provide an appropriate shim to pass key strokes to anything you want.

And just to be clear the appropriate secure model is to have a program request to register a "global" hot key and then the compositor passes it to the appropriate program once registered. This is already a thing in KDE Plasma 6 and works just fine.