Decentralized air-to-air heat pumps / Heating with air conditioners in old buildings

Says who, the energy certificate or actual demand?
I would first determine the heating load.

But that also means no solar gains. The windows are from which year?

First calculate (have it calculated), then act (buy).

I see a "kWh pit" here at first.

Where is the house located? In the cold east or the warm south?

Thank you also for this criticism.

The heating load was determined both by calculation and by energy certificate, the values were close together between 14,000 - 15,000. The windows are double glazed, also from 2000.
Although the heating load is irrelevant for the calculation mentioned above. This was about determining the cheapest kWh heat based on current prices of the sources. So even if the heating load value were wrong and the actual value much higher, one should still look at how to currently generate heat cheaply.
Later the heating load would be relevant for sizing the boiler.

I find the idea to rather calculate with a SCOP value of three good, that way one is more on the conservative side.

The house is located in Berlin.

The house is located in Berlin

If gas is available, you are no longer allowed to use oil or a liquefied gas tank.
Your options are then only gas or electric heating.

… or pellets (which is not meant as a recommendation)