Connecting magic mouse and keyboard to a KVM switch.

Let's start with a few "gotchas:"

• The Studio Display isn’t designed to be a multi-input monitor. Without a Thunderbolt KVM you’re essentially forcing it to behave like one; a number of Apple community threads repeatedly warn it’s happier when dedicated to one Mac.
• Some users report intermittent detection when flipping hosts (EDID/handshake timing). Keep firmware up to date, use short certified TB4 cables, and if a switch fails to wake the panel, toggle the KVM again or power-cycle the panel USB chain. Not very convenient.
• Windows can drive 5K/60, but camera/firmware/brightness support isn’t guaranteed.
• The Apple Magic Mouse over Bluetooth can be paired to multiple hosts, but switching isn’t as seamless as a single receiver.

Short version: sharing an Apple Studio Display between two hosts should be doable, but you’ll get the fewest headaches with a true Thunderbolt 4 KVM. If you try to “USB-C KVM + adapters,” you can usually pass video, but you’ll lose pieces of the Studio Display (camera/mics/USB hub/firmware updates).

AFAIK, the cleanest, one-button setup today is the Sabrent Thunderbolt 4 KVM (SB-TB4K)—it switches a TB4 upstream between two hosts and carries the display + the Studio Display’s USB functions together.

How I would set it up:

• Cabling:
  • TB4/TB3 from each host → KVM
  • KVM TB4 out → Studio Display upstream.
  • Plug your Magic Keyboard/Mouse (via a USB receiver or a USB-C→A adapter) into the KVM’s USB-A.

One button swaps display + camera/mic + USB together. Expect 5K/60 and full Studio Display features on macOS; Windows support for the Studio Display peripherals is hit-or-miss depending on drivers.

Unfortunately, since I do not have your exact equipment, I have no way to verify if this will work well for you ... so, think of yourself as a "beta" tester with this set up.