20% humidity in KFW 40+ new construction

You should best address my calculation if you think that opening the window would do something good for the humidity!

Your calculation applies to closed containers and not to a house, where there is already a 1 cm air gap under the doors and the windows are open at night.
Our house has 45-55% humidity without controlled residential ventilation, and there are also many flowerpots standing around here.

Your calculation applies to closed containers and not to a house

That is not correct. The calculation is generally correct. Of course, there are mixtures that then influence the humidity on average again. Basically, it is important to understand relative and absolute humidity. Then it quickly becomes clear that the problem is not fundamentally with the controlled residential ventilation, but with "cold, dry air." And letting this into the house through the window has only disadvantages and no advantages. By the way, you cannot retrofit an enthalpy exchanger on windows, but fortunately you can with controlled residential ventilation.

Our house has 45-55% humidity without controlled residential ventilation,

That is probably because you overall have a rather low air exchange rate, despite partly open windows. Or you bring in a lot of moisture through flowers, cooking, showering, etc.

I find the difference striking. We've been inside for 3 weeks now and I still ventilate several times a day because the (dezentrale) Kontrollierte-Wohnraumlüftung cannot remove the construction moisture on the medium setting. At first, we were constantly back at 60%, but it seems to be settling at around 55%. What kind of house do you have? Construction method, interior plaster, etc.

We have already turned off the underfloor heating and also kept the window open for a longer time (komplette Tag), but it doesn't help with the humidity. It hovers around 20%. We will now wait and see how it behaves when all the rooms are furnished / set up. For example, I still can't really use the kitchen properly and thus bring in moisture. But we have an air conditioner that will strongly dehumidify the air in the summer. Let's see how it feels in the house then.

First occupancy a few days ago 20% relative indoor humidity: In winter (when it is cold outside!) even if it is raining outside controlled residential ventilation on the lowest setting and windows not to be opened for ventilation! In spring/summer/autumn when it is warmer, windows open depending on the humidity/temperature of the outside air this will balance out over the next few months. The building materials/furniture/... must first be brought to a suitable equilibrium moisture content over time.

also keep the window open for a longer time

As described, in winter/with low outdoor temperatures, airing actually causes lower humidity inside the house. (Air warms up inside the house -> relative humidity goes down). That's why people say that something like drying screed and getting construction moisture out of the house is often easier in winter (if you air the room often enough + warm up inside).

I don't really have tips, my approach would currently be to counteract with smaller measures (plants, small indoor fountain, possibly humidifier where it bothers you most) and otherwise just wait and keep observing.