In case anyone is interested: I got my PC back from the store and they added a bunch of fans, but what I think really fixed it is that they changed the SVID behavior setting in BIOS to ‘Intel’s Fail Safe’. Something I overlooked myself… My PC is working normally now, no more internal compiler errors.
*EDIT: The friggin i9 13900K is still unstable. It may be overheating, although it has a high-end air cooler. Turns out that this problem returned after some time. I had to reduce the power limit drastically on this CPU in order to prevent it from malfunctioning. Latest intel CPUs really are a head ache. If you really make use of this CPU it turns out they are just unstable on factory default settings.