What will the building authority say?

What makes you conclude that? I referred to § 19 Baunutzungsverordnung when calculating.

§19 Baunutzungsverordnung, but since the resolution to establish the development plan dates before 1990, I refer to the Baunutzungsverordnung 1977 or 1968.

Where is the heating?

Attic/loft! In the technical room

It's almost a pity that I will be offline over the entire weekend, I'm looking forward to Monday

I see it differently, because in §14 it is said about the "anlagen" mentioned in §§2-13. Annexes are then introduced in §14, and in my opinion only those listed there are excluded in §19.

But, this is more a case for ... or rather a case for your company lawyer.

A street away in the area, a similar building was already constructed and the apartments were sold as condominiums. Everything without problems

The only problem there was, it had no elevator

A street away the area can already look quite different. The development plan is no longer accessible now, but I only remember one street line that was not further built to the west - except for your row of houses.

But I wouldn't care about that either: of course, I would be annoyed if 4 balcony residents/units were looking onto my terrace, and that is exactly what development plans are for, so that personal rights are not violated.

I have my doubts whether the staircase in that form is permissible. I have never seen this in a new multi-family house - a stairwell with spiral steps.

Yes, I have. Not uncommon in small multi-unit buildings.

I took a look at the property on Google Maps and I really had to smile: quite a lot has been built there in the meantime
There is even a supermarket across the street, the open field I mentioned is of course built on by now.... Yes, how old plans can be confusing