Yes, I'm aware USB-C is a plug shape, not a particular connection protocol. But Thunderbolt is compatible with DisplayPort. The M4 mini discussed here provides this support:
Thunderbolt 4 digital video output
Support for native DisplayPort 1.4 output over USB-C
An M4 Pro mini supports this:
Thunderbolt 5 digital video output
Support for native DisplayPort 2.1 output over USB‑C
When I had a KVM set up to use both an M2 Pro mini (and later my current M4 Pro mini), along with a 2010 mini to drive an older scanner, I used this cable.
But, I finally see what you mean. You weren't talking about an issue with a KVM or the M4 Macs, you mean the Apple Studio Display monitor itself. Then yes, looking again just now, I also cannot find any reference where you can use any type of DisplayPort cable. It must be Thunderbolt.
That really limits what type of KVM you could use. And I don't think I've ever seen a Thunderbolt KVM. You can find a few where the two inputs are USB-C (maybe Thunderbolt?), but they're all DisplayPort and/or HDMI out.
Would it be possible to use a KVM only for the keyboard/mouse (and maybe also share the audio), but have each Mac run its own Thunderbolt cable to the two video inputs on the Studio Display, then choose which computer signal you want at the monitor? I don't know if there are any soft keys on the monitor to do that.