How to efficiently plan heating for a new building?

BUT: Please remember that when using the cooling function, the humidity inside the house increases enormously. It then feels like a cool sauna.

That is not correct. I have had a brine heat pump with a cooling function for 4 years, which—when running—is always set to maximum power. - The cooling effect is about 3K with continuous operation 24/7; subjectively, that is a noticeable difference - The dew point monitor has never triggered, and condensation has never formed anywhere (mostly tiled floors) - The relative humidity indoors increases by a maximum of 10 percentage points at full cooling effect (electronic measuring devices in almost all rooms); this largely corresponds to the calculated change in relative humidity of the air cooled by 3K. I personally find the function great, especially since it uses only marginal electricity and has a clearly noticeable subjective effect. There is no question of a sauna. Of course, it is no substitute for a proper air conditioning system, but since the brine heat pump was already chosen in my case (not least because of the elimination of the outdoor unit and the BAFA subsidy at that time), the cooling was a bargain added on. Buying a brine heat pump solely for the cooling function is certainly not worthwhile; money is better invested in drilling for an air conditioning system. However, a brine heat pump can also be implemented more cost-effectively with a trench collector.

That is not correct.

- The relative humidity inside rises by a maximum of 10 percentage points with full cooling effect

That's what I'm saying. The humidity rises significantly. It feels terrible, especially in the muggy summer.

One can argue whether 10 percentage points are "significant." It definitely doesn't feel "terrible," but rather pleasant.

How is it when you cool with underfloor heating and then dehumidify somewhere in the house with an air conditioner: does the dehumidified air then distribute throughout the house via the [Kontrollierte-Wohnraumlüftung] or does the air ultimately go back outside without dehumidifying the other rooms?

How is it when you cool with underfloor heating and then dehumidify somewhere in the house with an air conditioner: does the dehumidified air then distribute throughout the house via the controlled residential ventilation, or does the air ultimately go outside again without dehumidifying the other rooms?

That should work, but it's idiotic. In that case, you might as well turn off the underfloor heating cooling and cool directly with the air conditioner.

Does the dehumidified air then distribute throughout the whole house via the controlled residential ventilation, or does the air ultimately go back outside without dehumidifying the other rooms?

A controlled residential ventilation does not distribute air. Extracted air goes outside, outside air comes in. There is no mixing in the heat exchanger.