It looks like you asked around on other forums as well, and got all kinds of answers.
I am shaking my head at some of the stuff you were told. Like on TH, for instance. That's bull. Ugh.
First of all, here's the thing: You're talking about a real bottom-of the-barrel PC. Even the RAM is one stick of 8GB DDR4.
But that's also the saving grace. Because cheap stuff is likely to be standard, not custom.
Now, I can't find pictures of the exact model you have, but I found this review of something that looks and reads like it on a German site (run it through Google Translate):
Einen günstigen Office-PC, der sich auch als Gaming-Rechner eignet? So ein Modell steht mit dem Medion Akoya P66089 demnächst bei Aldi. Kann er seine Versprechungen halten? Der Test!
www.computerbild.de
And if you peek at the picture and the video accompanying the article, it looks very much like a cheap two-memory slot mATX LGA 1200 motherboard, featuring a a M.2 slot, and powered by a crappy 250W PSU.
So if your computer is like this one, everything inside it will be respecting industry standards and can be moved to any other case, (mATX-sized and above. )
Now, whether that's actually worth the bother... It looks like you're in Europe, but prices can't be that bad even there!