Newly built apartment (KfW-55) cannot be cooled, always at least 25 °

But that's a Pyrrhic victory. For a minimum of evaporative cooling, you increase the humidity, which also makes it muggy.
A fan is completely sufficient.

By the way, I do it exactly the opposite. I run the dehumidifier in summer and accept the little bit of heat it produces for pleasantly dry air ;)

Perceived temperature (dew point) should not be underestimated. I would also strongly advise against the towel or ice cube solution, even if it is physically correct and actually produces evaporative cooling.

Perceived temperature (dew point) should not be underestimated. I would also strongly advise against the towel or ice cube solution, even though it is physically correct and does indeed create evaporative cooling.

It always depends on what one finds comfortable/uncomfortable. For me personally, a fan actually blows too much, which I don’t find very pleasant. I personally prefer a wet cloth over it.
But of course, the humidity is increased.

Today is August 26th, in this hellish month (today it is raining for the first time, the temperatures have been insane, always just blue skies, everything dried out). The split air conditioner has cooled the bedroom for 12 hours every night, and also repeatedly the office and living room. KFW55 house is otherwise hell in summer. I understand your tenant, it is simply unbearably warm and you cannot sleep well. Consumption: 56 kWh in effectively 24 days (we were not home for 2 days). Costs: 2.33 kWh/day = €0.7 / day. I would decide to buy a split air conditioner anytime again. The fear of dry air has not materialized, luckily I have not ordered any energy-consuming humidifiers yet. After the 12 hours of air conditioning in the bedroom, it is still >50%. Soon I will even heat with it – it is even cheaper than with the gas+underfloor heating…

KfW70 with monolithic 36.5 cm and double-glazed windows: actually consistently 23 degrees inside the house. When it was often over 30 degrees, the living room was sometimes 25 degrees because the patio door was frequently open. Otherwise, at night at least one window tilted open and early in the morning at 17-19 degrees ventilate and then close the shutters on the south and west sides during the day. I know why I didn’t build a KfW55 or 40... basically a plastic house with a ventilation system.

KfW70 with monolithic 36.5cm and double-glazed windows: actually consistently 23 degrees inside the house. When it was frequently over 30 degrees, it was sometimes 25 degrees in the living room because the terrace door was often open. Otherwise, at night at least one window tilted open and early in the morning ventilating at 17-19 degrees, then shutters on the south and west side closed during the day. I know why I didn't build KfW55 or 40... so plastic house with ventilation system.

Cool, that sounds normal. How is it with your heating and hot water? How many kWh per year?

I know why I didn't build KfW55 or 40... so a plastic house with a ventilation system

Timber frame with wood fiber insulation boards are not plastic bags. Always these generalizations... one bad, all bad...