Construction costs are currently skyrocketing

This is complete nonsense. The heating demand of a building is independent of the type of heating and of course a heat pump can provide as much heat to an old building accordingly. And it has nothing to do with fan heaters because the principle of the heat pump is used. The efficiency is about a factor of 4 higher than that of a fan heater.

Cop 4.0 with an air-to-air heat pump in an old building? Oh man! I don’t know such systems, but please explain, what supply temperature is the air supposed to have then? 130 kWh/m2, 150 m2 -> roughly results in a heating load of about 13 kW. With NAT, the building is supposed to be kept at temperature through air circulation. Let’s assume air supply temperature = 40°C Air density = 1.2 kg/m3 Specific heat capacity in kJ/(kg·K) = 1.003 results in 2340 m3/hour air circulation. With 2.5 m ceiling height, that’s a 6-fold air exchange rate per hour. Do you want ventilation ducts like in Real under the ceiling in your house? :D Apart from that, it simply won’t work with COP 4.0, With NAT rather COP 1.8 and then we’re already at a 13.86-fold air exchange rate :D If it were a proper old building with 250 kWh/m2 you would have almost replaced the air in the room every 2 minutes. Real hair dryer :P The air will be so unpleasant that you'd rather stay outside at -15°C. But I’m happy to be convinced otherwise.

I always read that it is best to convert to [WP] and underfloor heating. But that doesn’t make sense for two rooms in our house. In the bedroom and children’s room, the windows are open at night and during the day they are heated. How is the underfloor heating supposed to handle that? Does a "mixed heating" system make sense in an old building? [WP] with underfloor heating for rooms with a constant temperature and a second heating circuit with gas for "variable-temperature" rooms?

What is the bedroom heated for during the day?

The trick is quite simple, you temper the house evenly according to how you want it. What is the point of putting energy into a bedroom during the day and opening the windows at night because it is supposedly too warm?

Why do you heat the bedroom during the day?

The trick is quite simple, you temper the house evenly as you want it. What’s the point of putting energy into a bedroom during the day and opening the windows at night because it’s supposedly too warm?

There are supposed to be children who play in their rooms during the day and don’t want to be cold and sleep with the window open at night.

Then you just have to vent your more expensive energy out the window again.

No child I know cares whether the window is open at night. It is the neurotic parents who think that otherwise the child will get sick, die, or something else. Children, especially teenagers, manage perfectly well in their musty environment.