I built something like this. Luckily my monitor has an IR remote control, which allowed me to record and replay control codes to switch inputs. I used a USB hub

I built something like this. Luckily my monitor has an IR remote control, which allowed me to record and replay control codes to switch inputs. I used a USB hub that also had an IR remote control for my keyboard/mouse, and I used a teensy with an IR LED to send codes to both the USB switch and monitor. I used an IR repeater/extender to route the IR signal from underneath my desk where the teensy/usb switch are to the back of my monitor where it can reach the monitor’s IR receiver. I also made a little NodeJS app that shares my clipboard between my computers. Although the whole setup is pretty hacky, it works surprisingly well.