Any tool that switches screens, too? Essentially one terminal for n computers, with a hardware or software switch between them?
That would be a KVM. (not the Virtualisation software, but a dedicated Keyboard, Video, Mouse switcher). Good ones can be as expensive as ~£200.
I was looking recently and came across https://www.aten.com/gb/en/products/kvm/desktop-kvm-switches... (and similar in the range)
Switching multiple monitors simultaneously seems to take you into a whole new bracket I tend to associate with the 15-monitor fintech/daytrader market, with pricepoints to suit :(