I have now first made contact with our heating engineer, who is a master craftsman and can/is allowed to perform heating load calculations. The company has always been very competent and is more the type that doesn’t try to sell you anything you don’t need. He will call me back next week, ask for rough data, and then come over and take a closer look at everything. Whether I then have a heating load calculation done by an engineer, I will have to see. I also have two people lined up for that.
Yesterday I also read some studies and watched videos on YouTube, etc., and I think you are right that a heat pump + photovoltaics is the best choice. Our house also meets the requirements. One would just have to install underfloor heating on the ground floor, which we could then have done at the same time as insulating the floor towards the basement. Whether underfloor heating also needs to be installed upstairs remains to be seen. I would definitely not want to rip open the bathrooms (from 2017) for that. Upstairs there would then only be 2 children's rooms and a small hallway left. In the attic, it also doesn’t make sense since we hardly need to heat there at all and after the children move out, it will barely be used because we will then move down to the upper floor.
I am still completely undecided about the type of heat pump.