How do I share a studio display amongst multiple macOS machines? (without plugging/unplugging devices constantly)

How do I set up multiple macOS machines to use one or two shared studio displays?

I have adjusted my home computing model away from buying iMacs which Apple frequently pushes into premature obsolescence via limiting macOS upgrades, to a shared monitor model where I will have one or two Apple Studio Displays in my homes shared amongst various individual specific macOS machines.

In the past kvm switches or docking stations would suffice, but somehow it seems that the new Studio Display doesn't have enough capable ports or the intelligence to connect and identify multiple macOS devices. There doesn't even appear to be a third party who has come up with a Thunderbolt switch to toggle between macOS devices.

Simply put Apple seems to have built us a new home computing model centred around stand alone displays without the ability to share the display elegantly. I am likely missing some big ah-Hahahaha moment where there is a beautiful way to simply use handoff or something to share the display.., but as suggested I'm missing it.

Please advise.