House (built 2019) always warm April-October

If we keep the controlled residential ventilation running continuously in summer, it gets really warm inside the house. We have already checked everything. It brings warm air into the house.

I had that feeling with our controlled residential ventilation back then too. We also ran it at the lowest setting during the day in summer, and set it higher at night.

Very unlikely that a central controlled ventilation system leads to overheating in the house.
Also calculated here:
With active heat recovery, the temperature difference is at most one or two degrees.
For example, with us yesterday at 27 degrees outside, 22 inside, the fresh air temperature was 23 degrees.
So a 1-degree difference and thus about 50W "heating power." That is completely negligible.
With heat recovery deactivated, it would have been a 5-degree difference, so 260W.
Even that does not make the house totally warm, considering that a person already produces 100W of heat or a TV, computer, oven, etc. quickly emit multiple times that power.

By the way, shading inside hardly helps. Then the heat is already largely inside.
Shading east and west usually brings more than south because on the south side the sun stands so steeply in summer that it hardly shines into the windows!

I find that quite strange. Like others, although with numbers, say: a controlled residential ventilation system actually will not be able to heat your house. Yes, it is true that it is difficult to get heat out once it is inside. For this, for example, we had to sign (I don’t know what it depends on) that if we did not choose roller shutters on the south side, we would forgo thermal insulation. We were instructed accordingly by the architect. ... I skimmed through including your first posts. You have been at it quite a while, trying to become the master of heat by spring. When the sun comes around and basically shines through the windows, it already starts to get warm inside. With 10 or 12 sqm of windows you don’t always want to keep closed. Personally, I also like the warmth inside the house. However, of course it may also be that the amount of heat would put me off... for me, I notice that the upper floor seems to get more heat through fewer windows than the ground floor in the open plan area. I always attributed that to the smaller rooms on the south side, as well as the tree canopies that give shade in our garden, naturally also at the south side of our house... Maybe a heat-reflective film on your windows might bring some relief? How about planting one or two standard trees? The crowns don’t need to be lush – just enough to provide shade on the upper floor.

Very!

When do your roller shutters go down? Immediately at the "first" ray of sunshine or only after some time?

Unfortunately, we were not advised by the architect or the window manufacturer in this regard; they just presented us with roller shutters and we took them.

We never saw venetian blinds, unfortunately. There were just so many items on the list during construction, we didn’t even have that on our radar.

Therefore, you can plant something there again, although there are already trees in some form.