Wow, I seem to have caused a belief war here Anyway, many thanks for the interesting contributions!
In the meantime, I have informed myself at various places:
1. Consumer center, hotline: According to their view, air heat pumps are at best so-so, often do not work well because they are incorrectly dimensioned and used. They can become power guzzlers because they can only gain little heat at very cold outside temperatures and heat up with electricity. The roaster would personally prefer gas. The information brochure also views the air-to-water heat pump rather critically.
2. Energy advisor of the district: Air-to-water heat pump is not fundamentally bad. Gas itself is economical, but gas must be supplemented with, for example, solar thermal to meet the new minimum standard. No one knows how prices for electricity/gas will develop. His personal favorite (not specifically for us) is the wood pellet heating, especially if one is planning a fireplace anyway. With luck, one can use the same chimney, since wood/wood. In addition, the chimney sweep comes anyway twice a year because of the fireplace. And wood pellets (pressed wood waste) are a raw material that at least in the past was not particularly expensive.
He estimates the costs for gas/solar thermal at around €15,000, air-to-water heat pump around €22,000, and wood pellet heating at €25,000-30,000.
My interim conclusion: We will decide on a house plan. It will definitely have large windows facing south/southwest to enjoy a bit of natural solar heating in winter. Possibly play around with the roof overhangs to at least avoid overheating in the upper sleeping area.
Which system I will discuss with the energy advisors and suppliers – and in any case I will have the final offer checked again by the consumer center or the [Bauherren-Schutzbund].
Have a nice holiday evening!