In conjunction with a KVM for switching the USB between devices, you can use this software to automatically swap the inputs on the monitor (if your monitors support the command protocol, most do but one of mine doesn't support the "change input" instruction): https://github.com/haimgel/display-switch
Otherwise you'd need a KVM that supports 3 monitors which I'd imagine is a compatibility nightmare if they're beyond 1080p@60hz
I saw this a while ago and then promptly forgot about it. I should give it another try! I wish I could disable auto switching on my cheapo USB 3 switch though, sometimes my laptop will update and reboot and steal input from my desktop which is irritating.
Otherwise you'd need a KVM that supports 3 monitors which I'd imagine is a compatibility nightmare if they're beyond 1080p@60hz