Is the power consumption and procedure for screed drying normal?

When function heating, the temperature should be increased slowly. The idea is that the screed expands and contracts once, so you can see if it works or if it cracks.
There is nothing against going up to 40 or 50°C. Higher temperature means more water comes out. What you heat out now, you don’t have to get out later when you live inside.

A underfloor heating system needs exactly the supply temperature for which it is designed. And there are still plenty of general contractors and heating installers who, if the customer does not demand otherwise, take 38°C+ supply temperature, because then you can manage with significantly fewer pipes. This way, you can either offer it cheaper to the customer or earn more money.
Proper practice is there; there is no obligation to use 30°C supply temperature or less.

With your 270m² screed, about 3,000 liters of water were brought into the house, and that has to go out.
Tilt the windows open... may work, but not necessarily. Better to ventilate by opening windows fully 3-4 times a day and wipe dry.
In the end, I bought kitchen rolls and threw away the wet stuff; I couldn’t get soaking wet towels dry between ventilation intervals.

A heating device with 20kW of power obviously doesn’t run at 20kW all the time; it is temperature controlled because it has to maintain the 35°C target temperature.

Drying devices would cost you even more electricity... and you have to empty a drying device at least once, often several times a day.

Oh, by the way. Putting a heat pump on the screed—I have never seen that. The unit, including the 300-500L tank, weighs over half a ton.

PS:
And finally, 4 weeks longer until moving in will also easily cost you 1,500 EUR. Rent, construction period interest, possibly construction loan interest...

There is also nothing against going up to 40 or 50°C.

Let's rather turn it around. There is no reason for it today. Against it are the costs and unnecessary continuous load on the heat pump’s maximum performance. P.S. The state of the art in new buildings is currently a maximum of 35 degrees. Everything else is a misplanning according to the Building Energy Act.

Higher temperature means more water comes out.

Maybe even too fast? Is that good for the screed that was laid? Therefore formally: stick to the heating protocol (there are meanwhile some that only go up to 35 degrees).

Oh, put the heat pump on the screed, I’ve never seen that.

You have to look properly. With light devices it is placed on the screed or hung on the wall, only heavier devices go on a composite screed - but that is also screed.

The unit weighs over half a ton including 300-500l storage.

Don’t exaggerate. First of all, normal heat pumps don’t have such large storage tanks. If at all one is installed and not connected externally. The indoor unit for a heat pump starts depending on the model at 50 kg (e.g. Daikin wall-mounted without storage with 42kg). And hardly any device weighs more than 200kg (unless you already fill the storage).

The unit weighs over half a ton including a 300-500l tank.

And why do you need a filled hot water tank for screed heating?

Oh, placing a heat pump directly on the screed, I've never seen that. The unit weighs over half a ton including a 300-500l storage tank.

Even 500 kg should not be a problem for screed. I also have an indoor unit with a 500 l storage tank and was concerned for that reason. So I laid XPS instead of EPS under the screed and made the screed one centimeter thicker.

You do not place a wp on the screed because of the weight but because of the sound transmission.