The cellar has settled but the house has not? Gap in the prefabricated house

Only to a very limited extent. What you can see is apparently wool that is not rainproof visible, which needs to be fixed quickly. There is absolutely no reason to believe the house is floating.

Well, I didn’t say the house was "floating" either :-) But it looks as if the house is unevenly set. The gap where the wool is sticking out is quite large. What is the best thing to do about that? In the first picture you can see that the gap is smaller in the front and larger in the back. Isn’t that strange?

On the first picture you can see,

It seems to me that wishful thinking is at play here :-)

Are there no cracks inside anywhere?

I have the feeling that the [Kellerdaemmung] has shifted. Just a suspicion.

That a basement settles and the house above does not is rather unlikely.

If it gives you headaches, ask an expert.