I've done that with many games, even with some super old titles like Black & White. Factorio is the only game that has this issue.

https://www.amazon.pl/Bi-Directional-Switcher-Monitor-Splitter-Support/dp/B09Y5T7HRM?source=ps-sl-shoppingads-lpcontext&gQT=1
I use a device similar to this one to switch one of my monitors from pc to laptop and the other way around, and when I have Factorio on the screen that is being switched ...