Cooling in summer with air-to-water heat pump, underfloor heating and/or ventilation system?

I see no significant correlation there. The greenery may act like an additional insulation layer, so delaying, but it doesn't actually cool in the true sense. Underneath you still have another 15-20cm of insulation, possibly even more in some places (slope insulation). I don't think I bought ceiling cooling now.

If one takes article 19 as a basis, one can already speak of a cooling effect. One would just have to water the roof if there should be longer dry periods.

If you base it on post 19, you can definitely talk about a cooling effect. You would just have to water the roof if there are longer dry periods.

The only problem is that the cold has to contend with about 20cm of insulation through evaporation.

Correct, but if the heat from evaporation does not even occur to that extent, the house at least heats up less than a house without greenery. Houses usually heat up from top to bottom.

What are your experiences after a good year with the cooling function of your heat pump?

So our experience is very positive. It brings 2-3 degrees difference for us. The only thing that still doesn’t quite fit is the temperature across the floors. We don’t have individual room control. In winter it’s great, in summer it sometimes led to blankets in the evening on the couch downstairs so that it was comfortable upstairs. We now run them during the day on the photovoltaic electricity, even if it was only 2-3 kWh per day last year. If the controlled residential ventilation can’t manage it, then briefly the air conditioning for dehumidification, but it probably ran only about 4 hours last summer. We also have underfloor heating in the attic above the bedroom, which definitely has an effect downstairs.