Heat pump for room cooling in combination with split air conditioner?

Hello everyone,
we are currently planning the renovation of an older house or a part of it. In this context, a new heat pump (air-to-water) is also to be installed.
Since the renovation primarily concerns the upper floor and it gets quite warm there in the summer, the idea is to install appropriate air conditioning.
Now, new heat pumps can also be used via the underfloor heating as an "air conditioner" or to reduce the room temperature. In some articles, I have read that this is the most efficient solution, but the cooling is limited to a maximum of 4 °C and works very slowly.

Also – if I am not mistaken – with the air conditioning of the heat pump, every room or every floor is cooled. Control per room is not possible. Or am I wrong here?

I am now wondering whether it makes sense to install a split air conditioning system in addition or whether this is generally not done or advisable or completely uneconomical?

Does anyone here have any experience?

Best regards
Christian

Cooling through the floor works only to a limited extent even in new buildings. In a renovated old building, it is money thrown away.

You will need a commonly known split system. By the way, it is the same device that you also want to use for heating. However, it then acts on the air and not on the water in the underfloor heating.

Thanks already for the feedback. I spoke today with an air conditioning technician. He explained to me the issue of cooling via underfloor heating from a physical point of view. Cold falls from top to bottom >> Cooling via underfloor heating: the cold is already at the floor. He will now prepare an offer for my construction project. I am curious where I will end up. According to a rough estimate, it was about €2700 to €3000 per room...

Correct, that is why basically only the floor is cooled in this case, and one must also be careful not to fall below the dew point. Thus, cooling is already done in the wrong place, and then it must not be done to the necessary extent, because otherwise there will be problems with moisture.