What kind of soil is this? Are there any pollutants?

I have now ordered a test kit for asbestos. Has anyone of you had any experience with something like this? How much sample do I need to take?

Not much, cutting out a small piece is usually enough (about Din A 5). Make sure some of the adhesive is also on it, as it could also contain asbestos.

Why exactly was the apartment handed over like this?
Isn't it the landlord's responsibility to install a floor there?

Everyone can handle that as they wish. In Germany, there is freedom of contract within certain limits. If the landlord rents out the apartment without floors and the tenant agrees, i.e., signs, then that is how it is.

Of course, it's pretty stupid if you don't know what kind of subfloor is actually there. But rental apartments are scarce in many places, you take what you get... usually under the conditions the landlord envisions.