There is an open-source alternative however called Barrier that does exactly what I need: Share the mouse and keyboard between computers, shared clipboard.

There is a software called Synergy that can do this, but it is a commercial non-free product that is overkill for my needs. Of course with these you could also use just one monitor for the machines, but this is not something I need. Historically this is a physical switch that had a dial on which you could switch between the computers. I knew I needed something like a KVM switch, that allows using the same keyboard and mouse on multiple computers.