District heating does not meet KfW55 requirements?!

Personally, I see the greatest benefit in controlled residential ventilation with heat recovery

Sure, you have made that clear. However: My general contractor came with the great offers: €4800 extra for decentralized ventilation with heat recovery, and €11,000 extra for a central ventilation system. For the solar system with buffer storage, "only" €4000 extra. All costs split 50:50. Here, the pricing clearly predetermines the decision direction. For us, it will probably be clear. It's only about meeting the standard here. If someone said, "just pay €2000 more, then it’s fine and you get KfW55," that would be my preference. Generally, I like to choose systems and devices myself when buying and make comparisons. Here, you don’t know what you get and whether it will have any added benefit afterward. As long as there are no unnecessary follow-up costs, I see this simply as a main price increase of €2000.

A controlled residential ventilation system with heat recovery is listed here at 10-12T€. 11T€ as an upgrade is of course intense. If you can bite your lip, then accept the solution. If you are ready to argue, clearly say that the cheapest solution is okay, but you will not put any money into it. After all, KFW 55 is contractually owed. However, you would prefer if he calculated precisely once more how much the controlled residential ventilation would cost, because you would like to contribute to that...