Control climate with underfloor heating or via the ventilation system?

We had two air conditioning units in the apartment with [Kontrollierte-Wohnraumlüftung] - even 3-4 hours of continuous operation in absence led to a cool living room and bedroom - bathroom and children's room were still warm. Therefore, I believe that one single unit does not help - but it may also be due to the poorly planned [Kontrollierte-Wohnraumlüftung]... I will see it for myself in the future.

I never claimed that it is cozy... I only wrote that it is possible...

We had two air conditioners in the apartment with controlled residential ventilation – even 3-4 hours of continuous operation during absence led to a cool living and bedroom – the bathroom and children's room were still warm.

Therefore, I believe that one single device is not effective – but it could also be due to poor planning of the controlled residential ventilation... I will see for myself in the future.

I believe controlled residential ventilation does not bring much, but it also does not speak against an air conditioner, because the heat exchanger always works "towards" room temperature. The air exchange rate and heat capacity are too low.
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But it’s about comfort. If it’s uncomfortable, I don’t have to spend money (a lot!) on it and live with a few degrees more (or choose another concept).

Yes, I know the principle of [WRG], but if you only have air conditioning in one room, it will still receive heat from other rooms – therefore, I think the effect of cooling distribution is rather small. The opposite is also true, because heating only one room would only bring heat to the other rooms very slowly.

My main concern with the air conditioning was to create comfortable temperatures in the bedroom at night.

We have a bedroom facing south, and despite shading, it heats up quite a bit at an outside temperature of 30 degrees... so much so that in the first year I could barely sleep or not sleep at all. So the air conditioner was purchased and installed in the bedroom. The problem now is that if I only run the air conditioner for a few hours a day, the bedroom becomes relatively warm again at night... as Saruss correctly noted, the law of conservation of energy... so the air conditioner has to run until the room including furniture, etc. is really cooled down, which in our case means about 16 hours a day... so that I can turn off the air conditioner for the remaining 8 hours and sleep... in the morning after getting up, it is turned on again.

In doing so, I have noticed that the system (with 16 hours of operation) can supply the entire upper floor with cold air, but the other rooms heat up much faster again, although there is a temperature drop of 3-4 degrees during the day.

Hence the initial statement again... yes, it is possible to cool an entire floor with a single air conditioning unit. Whether it is inefficient is another matter. That is why I am also considering simply installing a ceiling cassette in the upper floor in the stairwell and then purchasing a 7 kW (or maybe 9 kW) system. This should then be able to cool the whole house.

Please keep in mind that a 9kw system also produces 9kw of cold air... You can't stand near the cassette for long! Even on the lowest setting, it cools seriously. I had a 7.4kw system, but in a Mediterranean country... Oversized can also be annoying. Put such a system on power mode, and it’s not far from being a cold storage. Still, you can't cool a 150 sqm apartment everywhere with it.