Floor area number of multiple parcels

Ok thanks for the hint. I haven't really looked into the topic yet. We are planning two full floors and a basement for storage, laundry room, etc., extra space in the basement as a gym or something similar. Does any of that then count as a residential basement?

Yes, as long as no restrictive conditions are mentioned in the textual provisions.

Double-checked: the development plan says nothing further about floor area ratio/plot ratio.

It is very unlikely that the two parcels constitute a single property in the building law sense.

I have seen this quite often in cadastral plans: buildings that extend over several parcels that have not been merged - however, usually then in village centers and built according to §34 or even before development plans existed.

Does any of that then count as a basement used for living?

A sports room could be a lounge. But you don't have to include it in the building application.

Buildings that extend over several non-united parcels

Although you can't see whether they are registered under one number in the land register or are legally linked by a consolidation easement.
Now, the words we used, "unlikely" and "frequently," are quite vague, so we could well be talking about the same facts.
However, this is irrelevant for the OP, as a consolidation is 99.9% unproblematic and, according to the cadastral authorities I know, is still done free of charge.

Whereby one cannot see whether they are registered under one number in the land register or legally linked through a unification building encumbrance.

Correct. In the mentioned cases, I had no shares involved and accordingly did not look under the respective land register’s cover, but only saw continuous units across several parcel numbers.