Bauhaus concrete villa with core insulation - experiences

That means you use air conditioning and [Kontrollierte-Wohnraumlüftung] as 2 separate, central units? For me as a layman: how is the distribution of the cool air carried out? Through a separate pipe system with separate outlets similar to [Kontrollierte-Wohnraumlüftung]? Or do you rely on split units (which I don't believe)?

We only have one pipe system. We have a large ventilation unit (Helios air1 XH series). In the supply air, an air conditioner is connected. Depending on the setting, the air runs through the bypass or over the heat exchanger.

Ok, thanks. So figuratively speaking, this means that controlled residential ventilation and air conditioning unit share the ducts and you either use the controlled residential ventilation unit or the air conditioning unit, and therefore the air conditioning part can be retrofitted. Did I understand that correctly?

Not quite
The ventilation unit always distributes the air.
When passive cooling is used, the air is only drawn in through the earth, guided through the bypass (so not over the heat exchanger), and blown into the house. With active cooling, the cooling unit also runs and the air also flows through the bypass.
With pure ventilation function, it goes through the heat exchanger.
So a pipe system, a large ventilation unit, and a large air conditioning unit.

Has only disadvantages for me. Why no separate air conditioning that efficiently cools the air only in the said room?

Because we wanted it cool everywhere. With this size, a central solution also makes more sense.