A high-cpu small machine will have noisy fans, there’s no avoiding that. The fans have to be of small diameter so they will spin at high RPM. Maybe you can say what you’re actually trying to run, and make things easier for us.

I gave up on this approach a long time ago and it’s felt liberating. My main personal computer is a laptop and for a while I had a Raspberry Pi 400 running some server-like things. All my bigger computational stuff is remote. So the software is self-hosted but not the hardware. IDK if that counts as self-hosting around here. But it’s much more reliable that way, with the boxes in multiple countries for geo separation.