Is it sensible to use a dehumidifier after taking over the building or just ventilate by opening the windows?

I assume that you have foregone a [Kontrollierte-Wohnraumlüftung]? A pity, hopefully you won’t regret it.

We had to turn off our [Kontrollierte-Wohnraumlüftung] yesterday because on cold nights it condenses directly on the supply air grille on the facade, damaging the new facade. It’s annoying and after less than 24 hours it’s already frustrating not to have ventilation.

But back to the subject: The devices you can buy for €350 are a complete waste. We also borrowed one like that from family and it pulled about 5 liters of water out of the building in 24 hours. That could have been avoided if you consider the electricity consumption in relation.

I assume you decided against a controlled residential ventilation system? That's a pity, hopefully you won't regret it.

We had to turn off our controlled residential ventilation system yesterday because on cold nights condensation forms directly on the supply air grille on the facade, ruining the new facade. It's annoying and after not even 24 hours, it's already frustrating not to have any ventilation.

But back to the topic: The devices you can buy for 350€ you can completely forget about. We also borrowed such a device from the family and it pulled about 5 liters of water out of the building in 24 hours. That could have been avoided if you consider the power consumption in relation.

No, we don't have controlled residential ventilation.

Well, the dryer and 5 liters in 24 hours have to be looked at objectively. Sure, 5 liters usually only fit in the collection container. When that's full, the device switches off. You empty it or attach a hose that drains the water into a larger device, then it pulls more.
The devices we have in mind are supposed to pull about 55 liters out of the building. Sure, that won't be exact, even if it's only 40 liters. Calculated over 2-3 weeks, that's quite a bit.
Apart from the electricity, which is naturally the other side of the coin, but still better than risking mold... the costs later are more expensive, aside from health... and we have a small child.

But the man from the blower door test still said there was a lot of moisture inside.

Yes, but that generally applies to every solid construction - it's just that the person mentioned it.

Nevertheless, there are certain rules for drying as well. You can't just start drying away recklessly, but for example must let it rest for 48 hours and then begin slowly. After the screed, for example, the rule was: start ventilating after 48 hours, only use a construction dryer after 2 weeks.

About the construction dryer: I don't know what you had there. We had one that extracted about 80 liters per day. You can't get it for just a few hundred euros and you could pick it up yourself. It fit in the trunk ;)
After one/two weeks, such a device is no longer worthwhile... but the moisture will still be inside for a year with you.

About the floor: the professional measures whether it is ready for covering.

You are thinking about it the wrong way. Please first invest in some usable hygrometers (from 12 euros), distribute them around the house. Then you will have reliable data and can decide.

We also do not have controlled residential ventilation, but trickle vents and our roof windows are always in ventilation mode. We always have the feeling of fresh air in the house. Before moving in at the end of April, we dried the house to below 30% humidity using a construction dryer. That took several weeks. Now in winter, we are happy if we do not go below 40%. Therefore, I would no longer endorse the frequent statement that a house always struggles with moisture in the first year.

Before laying the floor covering, the residual moisture in the screed should be measured.

but still better than risking mold... the costs are higher later, not to mention the health... and we have a small child

Again: You won’t get rid of all the moisture now by power drying, but through long-term airing, heating, etc.

The moisture that causes mold is generated when people live in the house, sweat out several liters at night (each adult up to one liter), cook, shower, and heat without airing.

No, we don't have controlled residential ventilation.

Well, the thing with the dryer and 5 liters in 24 hours has to be viewed objectively. Of course, 5 liters usually only fit into the collection container. When it’s full, the device switches off. You empty it or connect a hose that leads the water to a bigger device, and then it also extracts more.

I looked it up. The device we had costs €320 and is specified to 52 liters per 24 hours.
For us, it was not because we didn’t empty the container. The cheap device didn’t extract more than 5-10 liters.

Decent drying devices cost four digits.