If you assume 7500 kWh, that is annual heating costs of €525 with gas. Even with a 20% saving, you would need 109 years for it to pay off purely based on heating costs; with 50% savings (even 20% is not certain) it would still be 43 years... assuming that the kWh of the air-water heat pump really costs as much as gas.
So it’s not worth it.
I completely agree with you.
The bank also argued similarly to me.
Later I recalculated it several times with a good friend: The normal COP 3.x air-water heat pump and the gas boiler are (today) almost the same. You save the gas connection, which costs money. But the air-water heat pump is more expensive. At COP 3 and electricity costs of 20 ct/kWh, you end up at 6.66 ct. For that, I also buy my expensive gas.
Of course, this is a form of speculation: Neither you nor I know the future price development of energy sources.
Even though fossil energy sources are currently inexpensive compared to past years: Prices will rise again. An argument in favor of gas is that the reserves are still enormous. Disadvantage: fossil energy source, CO2 burden.
Electricity is supposedly at an advantage here. Currently, a little over 33% coverage is from wind power, hydropower, and solar in Germany (remarkable for a country at this latitude!). However, transmission losses of electricity are about 1:wild boar, the primary energy factor of gas is 1.1, that of electricity more than twice as high.
The adaptation of the grids (including direct current transmission networks, adjustments of local power grids,...) will be enormously expensive and is only just beginning; it will cost MANY, many billions until the measures are finished in (?) 25 years. These costs will be passed on to the electricity price. So I am almost certain: Electricity will at least not become cheaper, rather moderately more expensive. Here, the infrastructure plays a bigger role than generation costs.
Currently, the air-water heat pump is definitely worth considering (environmentally). Moreover, they facilitate KfW classification. Saving: You do not save money with it. The devices are expensive. You can practically be thrown a gas condensing boiler. When such a thing is worn out after 10-15 years, you can easily buy a new one. Also, I consider a gas connection in the house useful – there will also be interesting technologies that can compete well with air-water heat pumps and others.
But: None of us can see into the future... Let’s be surprised. We live today. In my opinion, everyone can make the decision pro/con air-water heat pump / gas condensing boiler according to their taste nowadays; from today's perspective, no one makes a mistake in either case.
Best regards
Thorsten