So, I have multiple monitors and multiple computers, and sharing a mouse and keyboard between them is apparently not easy.
However, I already built something a long time ago which can proxy keyboard/mouse events from a linux computer to another computer. Now I’m thinking that I can use that to build a mouse / keyboard sharing thingy. I don’t know what such a thing would be called, but let’s call it the MKST (mouse/keyboard sharing thingy) for now. 
The MKST would have a small computer, say a raspberry pi or similar that drivers it. Mouse and keyboard would be plugged into this small computer. On the computer there would be a program that reads the mouse and keyboard events, and sends them to to the right computer. (This is the thing I already built.)
My thinking is that insead of having some sort of button to switch between computer, I can tell the MKST about the screen layout, so that when the mouse pointer moves over the edge of the screen, it will just switch which computer the input goes to.
I’ll also need a button to lock it to the current computer, otherwise gaming will be difficult.
Overall it shouldn’t be that hard to do, and it will let me send my mouse / keybord events to any computer, regardless of what OS the computer is running. (As long as it supports USB devices.)