Can the air-to-water heat pump also be used for cooling in summer?

Only a sensible split air conditioner is any use there.

I have prepared it in four rooms, but it will probably come later due to our financial situation. Preparation costs maybe 300 euros...

Only a decent split air conditioner is useful there.

I have prepared it in four rooms, but it will probably come later due to our financial situation. Preparation costs maybe 300 euros...

Exactly! As I said... with us 7500 EUR including installation. The living room is 65 sqm in size. So it needs some power.

That doesn't really make the price much higher - the margins between the lowest and highest performance are usually around 200-300 euros per device. For four design devices from Mitsubishi, including the multisplit device, I pay around 4000 euros.

Why do you have air conditioners? With well-insulated houses, that shouldn't be a problem anymore, right?

Well-insulated houses can resist heat for some time; the walls store the heat in between and then release it again. But when a heatwave lasts for a prolonged period, even the best-insulated building eventually heats up, even through natural or artificial ventilation. Then it's over with comfortable 20°C inside the house. And then it also takes a very long time to get the heat out again.

Therefore, an A/C can make it more bearable under certain circumstances. We won't have one for now either, but we'll see if one is ever installed; it is considered if necessary.

That's exactly the problem ;) - and no matter how well insulated and summer heat protection is considered, at some point it's just warm in the place.

And then you "need" air conditioning - humidity is also still an issue.

In a new building, I would always pre-install one in certain rooms, i.e. run the necessary lines. Retrofitting afterwards is totally easy to do.