How to efficiently plan heating for a new building?

Not per se, but depending on the planning, it could work. Usually, for example, you don't have supply and exhaust air in the same room. Instead, you plan dedicated supply and exhaust air rooms as well as overflow areas. This would already result in a certain mixing. But yes, the idea is nonsensical. If it creates a dissonance that a large and expensive technical system is not used half the year, then you can also rely completely on air-to-air heat pumps (aka air conditioning) and use them for heating in winter as well. With good insulation, this works perfectly efficiently. Comfort is worse in winter but higher in summer compared to underfloor heating.

I thought with an enthalpy exchanger the humidity or dryness would indeed be somewhat retained between supply and exhaust air?

What happens 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 whole house via the controlled residential ventilation system, or does the air ultimately go outside again without dehumidifying the other rooms?

Yes.

That should work, but it’s idiotic. Then you might as well turn off the underfloor heating cooling and cool directly with the AC.

Not idiotic, because it works – for example, for me. I simply (still) don’t have AC.

I thought with an enthalpy exchanger the humidity or dryness would indeed be somewhat retained between supply and exhaust air?

That’s how I observe it in my case.

Despite all the cooling and dehumidifying here, we will probably install an AC next year. We already had unpleasantly high humidity so often this summer, which my dehumidifier had to fight against.

Not idiotic, because it works - for example, for me. I simply don't have (yet) an air conditioning system.

Did you read my post? Idiotic, because you first indulge in underfloor heating with cooling, but then additionally run an air conditioner to reduce the humidity. That it works is completely clear.

Despite all the cooling and dehumidifying I do, we will probably install an air conditioner next year. We already had unpleasantly high humidity this summer many times, against which my dehumidifier had to struggle.

That’s exactly what I meant. Only air conditioning is the more comfortable solution.

Can anything still be changed? Instead of a combination storage tank, I would prefer to use 2 separate tanks. Combination storage tanks often cause problems. The separation of domestic hot water and heating water with the different temperature levels does not work as well as advertised by the manufacturers. In addition, they are often integrated as a hydraulic separator, which creates additional problems.

Combination buffer + ERR is basically the worst-case scenario in terms of efficiency for new buildings and heat pumps. Even two tanks are not needed in 99% of cases. If the installer is stubborn, he may install a small buffer in series in the return line at most. Everything else is rubbish. For domestic hot water production: either a classic storage tank or alternatively a buffer + fresh water station (purely for domestic hot water, no combination storage tank). I would also always try to avoid a circulation line. Again, an efficiency waster.