Is it probably more of a general contractor, right?
The developer had actually promised us completion in KW 36, nothing happened, so we asked and were told that the craftsman was still on vacation but would come on 07.09.19.
That reads to me like you did not observe the official form and therefore the general contractor sees no need to act.
KW 36 was last week. The craftsman was on vacation until last Saturday and today is Monday and you are pondering.
Whether you are being strung along or not:
Write a defect notice by registered mail with possible deadlines to the general contractor.
If nothing happens, then issue a warning. Only after that can you commission a craftsman at the general contractor’s expense yourself.
Proper defect notices can be found online.
I have meanwhile considered a lawyer since I don’t know any other way forward, but that would be the last resort...
He wouldn’t be able to do anything else right now either.
Do you happen to know how it looks if we now assign the work to an external company regarding the warranty?
See above.
The defect notice is a process. If you don’t stick to it, the other party doesn’t have to either. It’s that simple.
What all else happened so that you are sitting in a house with a damp basement is already past. I always say: don’t build a basement, then it won’t get wet.
Regarding the other defects: were they documented in writing at the handover?
When was it?