At least one conventional air conditioning unit is usually needed for dehumidification anyway (otherwise the ceiling cooling switches off too early due to condensate formation). Therefore, I agree with the majority opinion here. The underfloor heating could be supplemented by concrete core activation.
For the air conditioning units (indoors), have a drainage system with a dry trap installed directly by the plumbing so that the condensate does not have to be pumped away. And of course, plan the drillings and slots for the [KM] lines in advance.