Could you tell me which eGPU you chose and why?
It might be on top of other complexities my unit is broken. It is also difficult to measure, because it doesn't behave the same way every time. There is clearly a random factor present. For example I might not always get fan noise if I do a test once for only 2 minutes. But if I do the exact same test 5 times (reboots or e.g. toggling ThrottleStop settings back and forth in between), I might get "bad" result 4 times and "good" result once.
I've got a Razer Core X Chroma coming in the mail, with a 580. It's about 50% the speed of a 5700XT, but should be plenty for my needs. About as fast as the internal 5500M, which is fast. I took the Chroma model, because it has an Ethernet port (new drivers from this Summer allegedly work) and USB ports + 100W charging, so it doubles as a dock. The fan and PSU are relatively easy to upgrade later, if I want to convert it to a silent unit, and I can later upgrade the GPU to 5700XT or whatever runs fastest & coolest in a couple of years. Apple approves this combo, according to the eGPU support page, and it's been common among Mac users.
As for a possibly faulty Mac, you could reboot while pressing "d" after the chime. It will run a hardware test. I doubt it reveals anything, but if it does, then you know for sure it's faulty and you'll have no trouble with the RMA claim. That's the same test that Apple Support would do. It's not an exhaustive test, but pretty comprehensive.