Renewal of heating system in old building, which system?

Yes, somehow an error in the system :-O But what kind?

Your house does not match the heat pump and the oil heating is effective. As I said, the rest should be calculated by professionals.

So now I have researched again and calculated the options:

CURRENT status oil heating with low-temperature boiler
With 2,500l oil consumption and approx. 11.4 kWh / l heating value for oil, that converts to 27,500 kWh / year.
With the oil prices (fluctuating), that currently means annual costs of approx. 1,150 EUR, if it rises again for example to 0.90 ct / l then approx. 2,250 EUR.. on average 1,700 EUR annually.

Air-water heat pump
If we were to use the offered air-water heat pump with a calculated annual performance factor of 3.9, then at a calculated heating load of 11 kW we would consume approx. 5,641 kWh / year of electricity. That is approx. 1,700 EUR per year at an average electricity tariff of 30 ct per kWh.
If the offered air-water heat pump is not as efficient as calculated and possibly only achieves an annual performance factor of 2.5, then at a calculated heating load of 11 kW we would consume approx. 8,800 kWh / year of electricity. That is approx. 2,640 EUR per year and 220 EUR per month at an average electricity tariff of 30 ct per kWh.

Gas condensing hybrid with solar thermal 8.5 sqm
If we switched to modern GAS condensing technology, we would probably only consume approx. 23,000 kWh / year of GAS. At the current GAS tariffs, that means annual costs of approx. 1,060 EUR.
If now a solar thermal system of approx. 8.5 sqm on the roof were installed, which offers approx. 15% heating support (actually theoretically 25%), then we could save approx. 3,450 kWh / year via solar energy. That means we would come to approx. 19,550 kWh / year and approx. 900 EUR / annually and 75 EUR monthly.

Conclusion:
That means for our described house - see - the GAS hybrid with solar variant would actually be the most economical, if a replacement via BAFA funding with 40% cost coverage is intended?

Important to know is that we also want to abolish the oil heating because it is over 30 years old and we want to gain the heating tank room as usable space. According to consultation with the municipal utilities, a gas connection costs about 2,000 EUR gross. But basically only 1,200 EUR, since it is also eligible for funding.

In my opinion, the high investment of the solar thermal system amounting to approx. 9,000 EUR gross still pays off within the framework of the 40% funding received. Annual gas costs of approx. 233 EUR x 25 years usage period = 5,825 EUR plus 9,800 EUR BAFA funding share for GAS heating parts, oil tank removal, house gas connection, radiator replacement, etc.. (24,500 EUR gross total costs) can be saved.
Am I correct with my calculation here? Or am I making a mistake in reasoning?

Maybe a professional can take another look.

Thank you all.

Best regards

As I have already written before and you yourself have calculated again. Your house needs about 27,500 KWh in its current state.

You have to divide this number by the annual performance factor to get your electricity consumption. With 3.9 you do not get 5641 kWh but almost 7000 kWh.

The heat demand of your house does not change just because you are using a different heat generator.

Even with a condensing boiler you need 27,500 KWh.

I didn't calculate it, but I wouldn't rely on the heating support. The system also has to be configured and adjusted almost perfectly there. My honest opinion: just have the smallest gas condensing boiler installed and that's it. Then carry out a thermal balancing in the first year and be satisfied with low costs. And I say that as a heat pump fan

As I have already written before and you have also recalculated yourself. Your house currently needs about 27,500 KWh. You have to divide this number by the seasonal performance factor to get your electricity consumption. With 3.9, you do not get 5641 kWh but just under 7000 kWh.

It will not be exactly like that. I think you can calculate with ~20-22 mWh. The 30-year-old oil boiler will not be efficient and is improperly adjusted.

If you assume the approx. 10 - 15 % savings that a condensing boiler can have, that roughly fits.

That's then approx. 23000.

Since you can't tell from a distance how good it was, I always assume the worst case. Especially since windows are already triple-glazed here and partial insulation has been done