Cooling with heat pump via underfloor heating?

We have roller shutters, we just didn’t expect such a high heat buildup (as you just calculated) from the pure sunlight through the windows during the first spring in the new house.

Yes, since retrofitting venetian blinds is usually very expensive and often not attractive, active cooling is probably the only option. Thanks to photovoltaics, though, it’s not quite so bad. ;)

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, 24°C inside (because of the air conditioning), and I then run the controlled residential ventilation, the house will get warmer again, right? The cooled air from the AC is transported outside, and the 32° outside air comes in? Then I have to use energy again to cool it down. Or am I thinking wrong?

Yes, keep it running, because that pretty much matches my figures. You need air anyway, and with heat recovery it’s only 25W of additional heat. With manual ventilation it would be much more! And your AC probably cools with 3000W or more. The one percent from the controlled residential ventilation won’t be noticeable in your power consumption, but you will definitely have better air.

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?