Air-to-water heat pump with cooling function - is the surcharge justified?

Hi, I want to have a prefabricated house built (2 full floors with a basement, 165 m2, timber frame construction). I was told that there is an additional cost of 5000 euros compared to the standard heat pump if you want to use the heat pump for cooling as well. Allegedly, it is quite an extra effort because thermostats/controllers have to be installed in all rooms. But Google says it should cost a maximum of 3,000 euros.

How expensive do you estimate the additional effort to be? Does active cooling with the heat pump even provide enough to make a noticeable difference?

For 5000 euros, I could probably have 2 split air conditioning units installed. However, the prefabricated house manufacturer does not offer an air conditioning system, and I imagine that preparing it for later installation is difficult. For me, a duct would have to be laid in the wall and a core drill in the stairwell would have to be made so that I can install the outdoor unit on the north side.

Thank you very much for the reply. Since it is a prefabricated house, the prefab house manufacturer will probably not be enthusiastic if I want to have cable ducts installed in its wall, as this would require cutting into the wooden beams.

What do you mean by the freezer chest? I know that there are freezers from Daikin, but they only work with an outdoor unit. I would be very grateful for a tip, as 5,000 € is quite steep.

Have you ever had the function running in your home? Can the parquet floor be damaged (condensation water), even if you watch the dew point?