Installing air conditioning --> KFW funding gone?

I am considering where preparation might make sense

Bedroom and stairwell or rather bedroom and living room.

and whether the controlled residential ventilation might also distribute the cool air somewhat?

No, physically it can only do so to a limited extent, or the effect is basically negligible.

A relief is provided by a geothermal heat exchanger. That means, in principle, the supply air of the [Kontrollierte-Wohnraumlüftung] is routed through a duct system in the ground, about 1 to 2 meters deep. In winter, the ground is around 7° and thus preheats the air; in summer, it typically has 12° and cools the air somewhat.

So it saves some heating energy, and the heating coil of the [Kontrollierte-Wohnraumlüftung] only switches on later. And in summer, the supply air in the rooms is cooler than without. The earthworks can also be done in [EL], then it only requires a bit more than the pipes. Some space is naturally needed for this as well, so in a terraced middle house it will be difficult.

But also occasionally hygiene problems... there are many who shut down the EWT again after a few years of operation, for this reason it is no longer hyped as much as it was 10 years ago.

Condensate drain at every indoor unit

And of course, it must be directed somewhere - either outside, if possible, or connected to the regular wastewater system.

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 a bit?

We decided on all living rooms, but it could probably be done more lightly. Distribution of the cool air through the controlled residential ventilation does not really work, just as a controlled residential ventilation system as a whole is not suitable for cooling.

No, physically it can only do so to a limited extent, or the effect is basically negligible.

We decided on all living areas, but it can probably be done more lightweight. Distribution of cool air through the controlled residential ventilation does not really work, just as a controlled residential ventilation system is not suitable for cooling overall.

Ok, I thought it would balance out similarly, since for example in winter there are no huge temperature differences between the rooms anyway. I am currently considering preparing the bedroom, children's room, and office. The living room adjoins the utility room, so something could still be done there later...

there's always room for more later...

Sure, but keep in mind that thicker pipes will need to be installed there.