There are Thunderbolt 4 KVMs now (can't speak to any myself, but they exist!). DSC will give you quite a bit of spare bandwidth with the Studio Display.
I've been using the Sabrent one for a year or so. It's worked quite reliably once I got the cables sorted. I was unintentionally using one TB3 cable in the mix, and that made it pretty flakey. It has been pretty solid since swapping that for a TB4 cable.