Air/Water Heat Pump Active Cooling

The goal with passive cooling is to extract the energy from the mass of the house (ceilings, floors, screed, ...). The heat is stored there; air is an incredibly poor heat storage medium, hardly relevant compared to screed and concrete ceilings.

That is why your comparison of briefly running the air conditioner is comparing apples to oranges. If you only cool the air down briefly when the mass of the house is already heated and then turn off the cooling, the air in the house will automatically warm up again within a short time because everything else in the house is still heated. You can only achieve a consistently low temperature if you cool continuously or at regular intervals, but not briefly (and then compare that to 24h continuous operation of passive cooling...).

In the end, it is about cooling performance per electricity consumption. With brine-water heat pump about 1:40 to 1:80. Unfortunately, linking is not allowed, but as already mentioned several times, there are quite extensive tests on this. They can be easily found by googling the forum in which the trench collector was also developed.

I am also familiar with these attempts. The concept, for example, of including the concrete was also tempting for us. I did not question the concept but also spent a long time dealing with it myself. It was not discarded for economic or ecological reasons but because we chose a different overall concept. It could not have been sensibly integrated here. Underfloor cooling would not have been an option since the woman always has cold feet anyway. Air is a poor heat storage medium or conductor. But this applies in both directions. However, the transfer of heat and cold is therefore also very slow. That is why it is faster and easier to cool the air. This is more important for us humans. For example, if I cool down the bedroom before going to sleep, it stays cool throughout the night. At night, the house also releases heat to the outside. As you rightly said, it should be a holistic concept. For example, shading, insulation, at night the controlled residential ventilation runs with an open bypass etc. Thus further cooling or less heating. We also pull the air through the soil so that it cools down further. Therefore, an air conditioner would not have to run continuously or only for a shorter time to achieve the same comfort effect. Therefore, the comparison is not off the table. With a brine-water heat pump you are more efficient when looking at the theoretical cooling capacity. Even better would be the whole thing in the ceiling or walls. Thus small cold feet and a greater effect. Ultimately, the perceived temperature plays the decisive role. That is the air temperature and humidity. And looking at these factors, an air conditioner (usually) makes more sense and is also no longer so energy-hungry. Compared to a reversible air-water heat pump it is probably more economical with simultaneous dehumidification and therefore a higher comfort factor. If the money does not hurt, he should invest the money. Usually, we are talking about low four-figure amounts. An air conditioner (with installation) is more expensive. Just don't expect miracles.

Many thanks for the many and detailed feedback, that has helped me a lot. I still don't know what we will decide on. But I do have a little more time. In any case, I no longer have to blindly trust the heating engineer.

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In any case, I no longer have to blindly trust the heating engineer

You should never do that anyway! No matter if it's a heating engineer, electrician, solar technician, etc.

That's what these great forums are for. Even if some claim that a lot / mostly nonsense is written in forums, it still helps to broaden one's perspective (wide angle )