Studio display with USB-C switcher.

I have an M1 Macbook. When at my desk I connect it to a Studio display monitor via thunderbolt, and everything is groovy. My work computer is a standard Lenovo windows machine. The video card has a USB-C port, and I can use the same cable to plug into it, and have the PC use my nice Apple monitor. This is also groovy.

What is not groovy-- because of how things are arranged, every time I do this I have to crawl around and get behind things. Granted, this is a first world problem, but I am lazy and my knees are bad. I thought, let's make life easier and just get a little switcher so I can just toggle the one monitor between two machines.

I just want to confirm this is one of those things that Apple thinks I don't need to do, right? Like, they want me just to buy a second monitor. I have tried several different switchers-- 100w/8k thunderbolt approved-- and still nothing. Why?