Newly built single-family house KfW55 standard - How to heat?

Of course, only it is not an advantage in a low-energy house in Germany. With a clay hut in the desert, it would be different.

Possibly also use in a 40 Plus single-family house - provided the overall concept is coherent -, right?

Possible, but probably not sensible. It is only a 40 house (which is not much better than a 55 house), not a passive house. High desired room temperatures will come at a corresponding consumption cost. There will definitely be no warm feet. Alternatively, you diligently poke at the wood stove.
Of course, it is significantly cheaper than installing conventional heating.

That is quite adventurous, electric underfloor heating. It reminds me of night storage heaters, which for good reason no longer exist.

Just consider: a house that is so well insulated requires very little gas. So you do not significantly harm the environment, have low investment and high flexibility. Where is the advantage of a heat pump? With solar, you also make your hot water free and environmentally friendly.

But the systems are ridiculously cheap, have no lobby in politics and have meanwhile been discredited by the Gretas.

My experience is: air-to-air heat pumps and even air-to-water heat pumps require excellent planning, execution and very careful commissioning. They should also only be used in Kfw55 or better. Then and only then is it an ecological, economical and comfortable way to heat your house. But there often remains the problem with noise both inside the house or with outdoor installation outside. Especially in the low-frequency range, there are often troubles with neighbors.

The practice (I know dozens of heat pump owners) looks unfortunately different. Most heating engineers fail at all the listed prerequisites. Leftover is a desperate customer who has invested a lot of money in a modern heating system, has high running costs and freezes in the bathroom in winter. Then the old fan heater can be brought out again.

The environment can also be pitied. Only the heating engineer and electricity supplier are happy, they are making a fortune.

Just think about it: a house that is so well insulated needs very little gas. So you don't really harm the environment much, have little investment, and high flexibility. Where is the advantage of a heat pump? With solar, you can also make your hot water free and environmentally friendly.

I totally agree with you. Personally, I would also prefer gas. However, in most new housing developments – like ours – unfortunately no more pipelines are laid.

So only the air heat pump, air-water heat pump, or the ground-water heat pump remain...

Especially regarding the cost advantage compared to using the additional heating element of the Proxon, we are now not so sure.

Despite extensive research, there are no real calculation examples on the internet. We have only found consumption calculations that assume that the electric underfloor heating is used exclusively as a heat source in the bathroom and thus requires 0.15 kWh/sqm.

Accordingly, the calculation of the monthly costs looks like this:

- 21 sqm bathroom (15 sqm and 6 sqm), of which only 13 sqm are to be heated (rest shower, bathtub, toilet, etc.)
- Consumption 0.15 kWh/sqm
- Heating duration including warm-up time: 1 hour in the morning; 2 hours in the evening

Means:
13 sqm x 0.15 kWh x 3 hours = 5.85 kWh/day x €0.30/kWh = €1.76/day

Let's assume that additional heating of the bathroom is necessary for 6 months (=183 days).

That makes – photovoltaic system with battery storage disregarded – €1.76/day x 183 days = €322.08 p.a. or €26.84 p.m.

Is that about right? Or are the costs lower because the electric underfloor heating "only" needs to temporarily heat the 21 degrees of the Proxon up to 23-24 degrees?

If you have to save, better leave out 4 sqm than do such rubbish...