Which heating system for a new single-family house

If possible, speed up.

Domestic hot water generation via air-to-air heat pump is a nightmare, the electricity meter spins with every bath.

In the end, the total of heating and hot water consumption counts, and it is almost irrelevant that the efficiency is lower for hot water production than for heating.
Every type of heat pump has this problem, and as far as I know, the efficiency of gas heating systems in hot water production is not ideal either.

expect option to be 10,000€ cheaper.

Yes, for the seller, otherwise they wouldn’t offer such a thing.

You just have to use Google once and find various homeowners complaining about their electricity bill. That is easily 1000€ p.a. more than necessary. And without heating surfaces, it can hardly be brought under control anymore.

I’m not saying it can’t work purely via air, but certainly not with a large prefab house provider. Even with KFW 40, I would only do it if I know exactly what I am doing.

If possible, hurry up.

Definitely with provider 1. A well-planned heat pump makes more sense in new buildings, unless it is offered at an excessive price or if insulation can be saved because of the heat pump, as this is then also sufficient for KFW 55.

Why is blown-in warm air not comfortable?

Why is supplied warm air not comfortable?

Because only a little heat energy can be transported via air. In the house < Passive House this means increased volume flow and/or high air temperatures. The latter further reduces efficiency. By the way, I am just realizing why you said in another thread that exhaust rooms are colder :)

Why is blown warm air not comfortable?

boxandroof provides the essential answer. Additionally, the counterquestion should be asked: what do you prefer more, heat from a fireplace or heat from the car ventilation? A bit polemical, but the basic principle fits.

With heat via preheated air, you always have inhomogeneous air temperatures. That is uncomfortable. Just like people on airplanes complain about cold air conditioning or people by an open window. Only here it is about heat, not about cold.