I've moved to Debian 12 just yesterday and when I downloaded Unity I was presented with a flickering red scene, I watched this tutorial that says to disable Auto Graphics API for Linux and move Vulkan above OpenGLCore.
It worked but whenever I open the project it closes after it loads, it doesn't seem like it crashed because when a Unity project crashes you get a pop up window.
The tutorial talked about the problem and his solution was to apt update and then apt upgrade, but that didn't work.