Installing air conditioning --> KFW funding gone?

That's exactly where the underfloor heating brings those few degrees. On the floor. But mostly you don’t lie there, you sit on a chair/sofa or lie in bed. Here the temperature is quite different again and you no longer notice those few degrees on the floor. Added to this is the humidity, which cannot be removed by the underfloor heating, and you haven’t actually gained anything with the much-praised cooling via the underfloor heating. If it means more than 200-300 euros extra, you can skip the add-on.

A few degrees would be enough for me, I’m not a Spaniard who sets the thing to 18°C :cool: I’d like the impression of SUMMER inside. However, I do not want to SUFFER from heat – and I see that time is working against me: Over time I’m not getting more robust, but the summers are getting longer and warmer.
I have often gotten ill from classic air conditioning because it strips the moisture needed by the mucous membranes. I find this property of retaining moisture combined with the direction DOWN from which the coolness comes quite pleasant. Like in a church in the Mediterranean region.

... and to provide some planting in front of the patio door? That’s actually the usual thing to do. It has proven itself for centuries.
You don’t always have to come with technology that makes the purpose and implementation more complicated.

Yes! Or build close to the forest, preferably on the northern edge. All possible.
You can also plant native plants, even better local, non-intrusive species adapted to the soil conditions, in your own garden. And wait.

A few degrees would be enough for me, I'm not Spanish who sets the thing to 18°C

Whether you have 30° or 28° in the room doesn't really make a difference. Others have already had to realize that.

It is also allowed that the impression of SUMMER arises inside.

Right. That is perfectly compatible with air conditioning.

I have often gotten sick because of classic air conditioners BECAUSE they withdraw the moisture needed by the mucous membranes.

Same here... It is always assumed that the systems are binary, meaning they can only be cold or not. The truth, however, is that they can have many intermediate stages, and if you call such a system yours, you can gladly adjust the amounts as best suits you and your housemates. The illnesses come from lack of maintenance, too large temperature differences, and simply devices set incorrectly in a trivial way. The ones in the large (retail) stores are simply set to 16 degrees and that’s it. Regardless of whether the customers complain. The majority are nevertheless satisfied.

Only one indoor unit. However, we have a large airspace opposite the bedroom, so a lot of cool air flows into the lower floor, which is designed as an open space. Unfortunately, the children's area does not get much of it. You can use a standing fan to blow the air over during the day. It's not the best solution, but it's doable. If I were to build again, I would take a second indoor unit.

In how many rooms do you have an indoor unit? I am considering where a preparation might make sense and whether the controlled residential ventilation might also distribute the cool air somewhat?

Ultimately, it depends completely on the floor plan. However, the controlled residential ventilation does not distribute much and is virtually switched off during the day and works at night with an open bypass.

Is your garden already finished or is it still possible to build an air well for the controlled residential ventilation?

For centuries, houses were built differently than they are nowadays.

However, you don't necessarily have to use a sledgehammer to crack a nut when a simple flick would suffice ;)