Renewal of heating system in old building, which system?

No, you are right, I had forgotten that there is also funding for gas hybrid in the existing building. Therefore, I would also tend towards gas here. Savings referred to the 45% or 40% funding, i.e. I would invest the money from the funding in insulation and possibly new underfloor heating. However, I would have that recalculated to see how much it actually brings.

So you mean that the GAS hybrid variant (condensing boiler) with 8.5 sqm solar thermal on the roof for heating support is the better choice? I am also planning to replace the windows on the first floor via 430 (individual measures) with a 20% subsidy. Through this program, the insulation of the top floor ceiling could also be done. But the question is whether anyone has experience with what that costs? Especially the ratio of material to labor costs. It might be worthwhile to forgo the subsidy and do it yourself if the labor costs greatly exceed the material costs. Roughly calculated for 100 sqm area, I came to costs of about 4,000 EUR (3,200 after deducting 800 EUR subsidy) for walkable insulation. Is that accurate? So I have also considered installing underfloor heating (which is also funded at 40-45%), but I am somewhat reluctant because of the additional costs, since, for example, the floor coverings would also need to be renewed. I checked Google, and for example, for dry systems with 91 sqm it says about 6,000 EUR? Then another 6,000 EUR for floor coverings, so that would be about 12,000 EUR, of which only 45% would be funded for heating with heat pump. That would then only be 6,600 EUR. If, in addition to the described measures, now all windows were new, the top floor ceiling insulated, and underfloor heating installed over the entire living area of 186 sqm... would a pure air-water heat pump then be worthwhile? Best regards

If besides what has been described, now all the windows were new, the top floor ceiling insulated, and underfloor heating installed throughout the entire living area of 186 sqm... would a pure air-to-water heat pump then be worthwhile?

Off the top of my head: Yes. You save on the gas connection. Have you already considered installing low-temperature radiators for the heat pump instead of underfloor heating as an alternative? That way you also save the underfloor heating and floor coverings. You have to calculate whether the radiators are sufficient. You should do that – unless you want to do everything completely and have enough money to spare.

What do you actually want to achieve?

Savings on heating costs, or is the old heating system broken?

Gut feeling: Yes. You save the gas connection. Have you considered installing low-temperature radiators for the heat pump as an alternative to underfloor heating? Then you also save the underfloor heating and floor coverings. You need to calculate whether the radiators are sufficient. But you should do that – unless you want to replace everything completely and have enough money to spare.

Well, a company would install the GAS hybrid solar thermal system with a GAS connection for about 34,000 EUR, remove the old oil heating system and tank, and convert seven radiators (for 55 degrees flow temperature).

Regarding the heat pump, we are torn back and forth because of the noise of the outdoor unit with an air-water heat pump. One is supposed to be from Viessmann or WOLF.
Also, the uncertain electricity demand at least during the heating period is uncertain.

What do you actually want to achieve?

Savings on heating costs, or is the old heating system defective?

Savings on heating costs and gaining the basement space (where the oil tank is) is the plan. The old oil heating still works, but it is almost 30 years old.

Viessmann low-temperature radiator type 21 500x600x218 mm (H x W x D)
Look up and google low-temperature radiators or low-temperature heating radiators. A flow temperature of 30 degrees is sufficient. Which one you exactly need must be calculated. My example is about €550. But you don’t need the underfloor heating and floor coverings.

because of the noise of the outdoor unit in air-to-water heat pumps.

Walk through new residential areas and listen to them. From spring to autumn you won’t hear anything anyway, as they are hardly on (at most for hot water).
In winter, you are at least inside the house. Outside, they are nowadays very quiet (the neighbors are also inside in winter and don’t hear anything).

The uncertain electricity demand at least during the heating period is uncertain.

Do you know the gas consumption in advance? That is just as uncertain.

Okay if you want to save on heating costs you have to insulate.

The „ Energieverbrauch „ in your house depends to a very large extent on the insulation standard and not on the heating system.

First you need the current condition of your house and the materials and insulation thicknesses.

To get a rough overview you can then use a U-value calculator. Just search the term on the internet