Additional costs for a prefabricated basement in a KfW40 house and a prefabricated basement

If I were to close the outdoor seating area, then enclosed space would also arise exactly on this boundary.

I don't see it as significantly far from that even now.

But you probably mean the additional costs only for the house and not the basement, right? My question is whether the basement becomes extremely more expensive due to KfW40.

The majority opinion here is that the upgrade, even when related only to the house, is a very symbolic benefit—and if you then also raise a non-residential basement to this level, it rather "isn't worth it" if not "pious, but luxury."

...But if there are massive additional costs here, then I have two options: KfW55 with basement or build something larger than KfW40 without basement...

I can imagine that there are certainly more than your 2 options here.
If KfW "something" is planned, you will need an energy consultant anyway. Just ask one of them non-bindingly what they charge for calculations, applications, and construction supervision (in the area of "energy").

Maybe it is possible to create a "cold basement" outside the thermal building envelope separately and not include it in the KfW calculations. Only then must the basement be well thermally separated (insulated basement door, basement ceiling, etc.).

My property is quite flat. I want to build a basement because I need the storage space.

I am a committed member of the faction "in dubio pro Keller," but here I have no doubts, here it would be a luxury. Just what the basement costs even without additional insulation effort and energy consultant services, you can rent two garages for life.