New building: Which insulation is appropriate?

Hello,

...No, actually a KfW 70 house, since we want a gas heating system, but with a SENSIBLE, possibly better insulation - without overdoing it.

As the construction expert has already described, you can also include an air heat pump in your considerations. Provided the framework conditions are right for it.
This can possibly achieve KFW 55 and make solar unnecessary, basically saving twice!

Best regards.

Hello,

we definitely do not want a heat pump here in the north.
Then I am more likely to consider a cogeneration unit...

And a passive house has not quite convinced me of its functionality so far. It usually does not work completely without an additional heating system.
However, I have now read about passive houses that also have solar and an additional gas heating system...

One could go in that direction.

Hello,

...Then I rather think about a combined heat and power plant...

A combined heat and power plant is usually not economically worthwhile for a "normal" single-family house or two-family house. The problem is the unused heat outside the heating period. Just calculate (have calculated) an energy balance.

Best regards.