Cooling with heat pump via underfloor heating?

You mainly need it in winter. In summer it is useless.

Yes, but only if an imbalance exists. If moist air already comes in, then it can’t regulate anything. Moist air out -> through the moist enthalpy exchanger -> new moist air in. Result in summer -> moist air everywhere. In winter no, because then there is a temperature difference and the moisture can be regulated and raised a bit by the exchanger, so it doesn’t fall to unexpected lows in the house.

No, that’s just marketing talk. Sure, later you bring in slightly cooler air but the amounts are negligible. RotorMotor explained it quite well.

No, that’s more wishful thinking. Underfloor heating-cooling only gives you a somewhat cooler floor but hardly cooler air in the house and above all the moisture remains. 4 degrees is utopian, unless the house is in the woods and hardly gets any sun.

These are calculated values. In practice, we have experienced that without air conditioning, you cannot keep 23 degrees inside the house when it is 30 degrees outside. Unless you shade yourself like in a bunker. In practice, it also gets warmer inside the house, and the problem then is that with heat recovery you can no longer get the temperature down.

With us, the temperature control via underfloor heating costs around €4,000.

When I asked what you would advise me, the first thing was tempering via underfloor heating and the up to 4 degree temperature difference.

Insulation neither lets heat in nor out,

For us, the temperature control via underfloor heating costs around €4,000. The most expensive part is probably the switches. We have it included in the price. In addition, we will process it through BAFA. We should then get 35% back, I think.

When we built, I also considered the air conditioning more of a luxury. Now that the first summer in the house is underway, I am really glad to have it. Because it is very difficult to keep the heat out in such a well-insulated, new house. Already just the sunlight coming through the windows heats up the house. You either shade so thoroughly that you could live in a cave, or you let the light in. The amount of heating energy that 1 meter of window front with sunlight provides is not to be underestimated; I massively underestimated this during construction.
And once the warm air is inside the house in summer, it is difficult to get it out again without air conditioning. The only thing I can think of is not ventilating during the day and then trying to get the warm air out at night through ventilation.