Cooling with heat pump via underfloor heating?

And at night when the photovoltaic system doesn't produce any energy and there are still tropical nights, do you turn off the air conditioning?

Yes. The heat doesn't come in because of the warm outside air, but because of the sunlight that comes in through the windows.
Since there is no sun at night, it hardly gets warmer inside the house at night either. We just make sure that during the day we reach/maintain the temperature so that the bedrooms are already comfortable for the night.
We also don’t run the air conditioning for 5 hours a day here. The units are quite powerful; usually a few minutes are enough when you notice that it’s slowly getting too warm. Upstairs we only have one split unit for the entire floor; in the afternoon, we then open the relevant doors and let it run for about half an hour to an hour.

Yes, keep it running, because that corresponds quite exactly to my numbers. You need air anyway, and with heat recovery it's only 25W additional heat. Manually ventilating would be much more! And your air conditioner probably cools with 3000W or more. You won't notice the one percent through the controlled residential ventilation in electricity consumption, but you will definitely have better air.

How do you come up with these 25W? The ventilation system does not change the temperature of the outside air it pulls in, right? Or does it? If it's 32°C outside, the system pulls 32°C warm air into the house too?

Would you keep the controlled residential ventilation running normally in summer? We don't have a summer cassette, so it runs with heat recovery. If it's 32°C outside, inside the house (because of the air conditioning) only 24°C, and I then run the controlled residential ventilation, won't the house get warmer again? The air cooled by the air conditioning is transported outside, and the 32°C from outside comes in? Then I have to use energy again to cool it down. Or am I thinking about this incorrectly?

The cold air flowing out cools the incoming warm air. A heat exchanger works both ways.

How do you come up with these 25W? The ventilation system doesn’t change the temperature of the outside air it pulls in, does it? Or does it? If it’s 32°C outside, the system also pulls 32°C warm air into the house?

Yes, it pulls 32°, but this is cooled down via the cross heat exchanger.

Upstairs we only have one split unit for the entire floor, so in the afternoon we open the relevant doors and let it run for half an hour to an hour.

And is that really enough?
Would you tell me how many rooms or square meters you have upstairs and what kind of air conditioning it is, so that the 'open-door technique' is sufficient?

And is that really enough? Would you tell me how many rooms or sqm you have upstairs and what kind of air conditioner you have, so that the 'open-door technique' is sufficient?

It might also depend on what standards you have. So we don’t cool the bedrooms down to 18 degrees. We have a Mitsubishi air conditioner, I’m not exactly sure about the exact model, I think SCM 50, with 3 split units SRK 25. 7100 watts cooling capacity in total. Upstairs we have a bathroom, parents’ room, and 3 other rooms. None of them are huge. Currently, we only open the doors to the parents’ room and one child’s room. I like it warm in the bathroom, and the other two rooms are currently used too rarely to keep them cool. For us, the staircase is near the split unit, which has the effect that once the rooms upstairs have cooled down, the hallway downstairs is also noticeably cool. That’s hard to prevent because the cold air naturally wants to go down. ;) But it still distributes sufficiently. We were worried about that at first too. During the planning phase, however, our contact person said that with such a system they cool the entire exhibition rooms and that it has quite a lot of power. We trusted that and see it the same way now. Regarding the note about colds/unpleasantly cold drafts: I also had such problems often when we were somewhere on vacation where it was insanely hot and there was an AC in the room. When you have your own system, you get a feel for it over time. It has proven effective for us not to set the remote control directly to 20°C — even if the effect is of course amazing when you are sweating and then ah step into the cool air. After the initial hype became habit, we now set the device rather to 23 and let the rooms cool down more slowly, plus we cool immediately when we notice it’s getting a bit too warm (usually from 26-27), but then only briefly until it’s comfortable again.