Which BHK block heating power plant - costs?

The prices for heat from a combined heat and power plant are not excessive, rather inexpensive, especially when compared to a local heat network. In a heat network, of course, you have a large investment share in the network construction, which should be significantly lower in such a project.

The factor that might be decisive for the provider: with a combined heat and power plant you will achieve a primary energy factor of 0.3-0.5, and if it is a somewhat larger one with an appropriate electricity ratio, possibly even 0.0. Additionally, you thus meet the share of renewables required by the Renewable Energy Heat Act. This way, the provider can achieve KfW 55 or better without much additional technology, or at least meet all legal requirements without solar thermal or similar.

if I still have to pay a higher 5-digit amount until the end of life in my simple calculation with the basic data I have compared to the gas boiler

I would check the basic data once - the gas boiler does not have the efficiency of a combined heat and power plant, at 5 MWh the house will stay cold. Better calculate with at least double the amount, you will hardly get by with less than that with a gas boiler. You also forget the annual costs for the chimney sweep and inspections, which you have to have done at least during the warranty period. Whether it ends up being somewhat more expensive or cheaper is crystal ball reading. In any case, the difference is not significant.