Ok, I completely agree with you about oil. That is really no longer quite up-to-date, especially because of the smell and space requirements.
Chimneys are now completely omitted with gas as well, it goes outside through a plastic pipe (costs max. 100€). The gas tank installation costs 4,000€, so it is correct that the initial investment exceeds that of the heat pump. However, the latter is more expensive than the gas heating system, but I don't have the exact difference for you.
Effectively, the price advantage for the heat pump should be somewhere around 1,000 - 1,500 €, if you build with a general contractor, the difference is probably rather on the side of the gas heating system.
And the most important point for us was reliability. Gas heating is a proven technology, heat pumps have been installed on a large scale for a maximum of a decade. They are definitely more prone to defects, and in operating costs at best ahead in the manufacturers’ bills. The real consumption values are actually significantly higher.
We heated our house last year with 560€ of liquid gas (129m2, 4 people) and produced hot water.
Let’s assume that the kWh costs only 22 cents, then I get 2,545 kWh for that. The heat pump can't manage that, can it, or can anyone provide concrete figures here?