New building with underfloor heating, residential ventilation, and air conditioning

I built almost the same way and would do it again. Well, no. By now I would build passive and save myself the part with the heating. But of course definitely with air conditioning!

When planning, remember that a new building has similar "cooling loads" to heating loads. So if the heating comes with a total of 4 kW (if it's more, either the heating or the house is wrong), you don't need an air conditioner with 3.5 kW in every room. Usually, at the highest point in the house a 2.5 kW unit is sufficient, which you simply run comfortably on a low setting. Assuming open doors, that is the quietest, cheapest, and draught-free way to keep an entire house at a pleasant temperature. Of course, that doesn't work if I have unshaded skylights and only turn on the air conditioning after work.

On the topic of "proper shading": Of course shade. But unfortunately, that doesn't help with humidity at all. 25° at 35% humidity is fine in a T-shirt. The same temp at 75% is just muggy.

It works just as well the other way around. The required cooling capacity is equally manageable.

To get the heat out, yes. But if the sun continues to blaze through the nowadays common large glass surfaces without hindrance, a standard air conditioner would probably be overwhelmed, wouldn't it?

Another "problem" with modern houses is that the insulation doesn’t only work in winter.

I can already confirm that now, I currently live in a converted attic apartment from 2016, which is super insulated (it used to be a cold roof). When all the blinds are closed, I also have cool temperatures here in summer, but if the balcony has been open for too long, the heat stays in the room o_O

Only if the sun continues to blaze through the nowadays usual large glass surfaces unhindered, an off-the-shelf air conditioner would probably be overwhelmed, right?

Why should it? It’s also possible to keep the same houses warm in winter at double-digit subzero temperatures. As already mentioned, it works just as well the other way around.

Admittedly, you’re fighting against a huge thermonuclear reactor called the sun, but it provides the necessary power exactly at that moment.

The system must of course fit the house, and as Deliverer already said, a standard device with 2.5-3.5 kW may be sufficient. Powered by photovoltaics. We don’t build cardboard houses like in the USA nowadays, and there’s no more draft around every corner like in grandma’s days. So heat stays inside despite shading (without shading, a modern building is simply a sauna). Ventilating this heat is more or less pointless. Moisture adds to the difficulty. A simple and inexpensive solution is active air conditioning.

If all the blinds are closed, I also have cool temperatures here in summer, but if the balcony was open too long even once, the heat stays in the room o_O

Well, then you’re well informed about what a modern house is... regarding insulation, temperatures, need for ventilation, insulation, and infiltration, etc. etc.