Is it possible to retrofit air conditioning if controlled residential ventilation is available?

Hello,
we live in a KfW55 house with [Kontrollierte-Wohnraumlüftung]. Since it is simply too warm for me in the summer, I would now like to retrofit air conditioning units.
I have planned a total of four units. In the three bedrooms on the upper floor, as well as in the open living, dining, and kitchen area on the ground floor.
I have looked at the units from Gree and would choose 2.7 kW units for the upper floor and a 5.3 kW unit for the ground floor due to the room sizes.

Now to the actual question:
Does an air conditioner make sense if we also operate a [Kontrollierte-Wohnraumlüftung]? Do the air conditioning units generally need to be sized larger because the [Kontrollierte-Wohnraumlüftung] removes the cool air too quickly? Or does the [Kontrollierte-Wohnraumlüftung] first prevent the rooms from cooling down at all?

If you want air conditioning yourself in this below-average warm summer, perhaps something is also wrong with the thermal insulation. Is shading consistently done during the day? And is ventilation done at night?

I live in the Rhine Valley, where it is always among the warmest places in Germany. At the moment it's okay, but 30 and 40 degrees are coming again. When it is 26-27 degrees in the house, it is too hot for me. I am a winter person.

The controlled residential ventilation generally does not cause any real problems. It could be automatically reduced to minimum ventilation when the air conditioning is in operation.

However, the entry of a usual controlled residential ventilation is negligible. Assuming your controlled residential ventilation runs at minimum ventilation at 100cbm/h, that is the amount that a 3.5kW air conditioner cools down in 10 minutes. So, not worth mentioning.

How big is the house, that is, how much air needs to be circulated?

So the house has a little over 1,100 cubic meters of enclosed space. The ground floor and the upper floor have about 800 cubic meters. At the normal level (2 out of 3), the controlled residential ventilation runs at about 150 cubic meters per hour.

I looked at the devices from Gree and would choose 2.7 kW units for the upstairs and 5.3 kW units for the downstairs based on the room sizes.

If your rooms are not huge, that seems quite a lot to me. What floor areas are we talking about here? At a total of 13.4 kW, the outdoor unit won't be cheap, or are you talking about single-split units?