Which heating system for the new building (prefabricated house)

Air-to-air heat pump is very interesting for the provider because it is relatively inexpensive to build.

Thanks, I have researched that by now as well. The question is always the sensible alternative. But I do not want to hijack the thread here.

and relatively high margin... water-bearing wood-burning stoves are more for old buildings, here the additional investment in new buildings is not worthwhile at all

In my case, the chimney/wood-burning stove (not water-bearing) would be supplementary to the underfloor heating.

We signed the purchase contract for our house last week; all 5 [FH-Anbieter] had planned an air-to-water heat pump. In the end, we bought a Kfw 40+ house with photovoltaics, controlled residential ventilation with heat recovery, a house without a basement from a smaller provider in solid wood in Upper Swabia, whose overall concept absolutely convinced us – also in terms of price. The heating is done with geothermal baskets and a corresponding heat pump without an additional heating element. The air-to-air heat pump or air-to-water heat pump has the worst efficiency when the heat demand is highest; there are also very different experiences in the forum regarding energy consumption and COP. Without additional heating, I would definitely not do it, especially not in cold regions.

a KFW 40+ house with photovoltaic, controlled residential ventilation with heat recovery,

For KFW 40+ you still lack the (unprofitable) storage and the management solution/virtualization. Check your documents again, because if not included, you have to calculate >8,000€ extra, alternatively expect 5,000€ less subsidy.

Hello Alex85, the unprofitable storage is already included in the purchase price, as it is mandatory for 40+. Due to 2 apartments, there is 2 x €5000 extra repayment subsidy and thus the storage is paid for....