KfW40+ with a basement inside or outside the thermal envelope?

But you can't sign a contract if it's not at all clear that your wish is feasible.

I assume that both are "feasible," each probably having its advantages and disadvantages.

Provider 1 probably thinks it is "cheaper" (possibly also easier for the seller) to design the basement outside the thermal envelope, and the insulation between the basement ceiling and the ground floor achieves KfW40 efficiency. However, additional insulation is still needed under the basement slab since a floor heating system will be installed for the music studio, which will take up about 33 sqm (about one third) of the basement.

Provider 2 probably thinks that if there is already floor heating and controlled residential ventilation in the basement, it is better to insulate under the basement slab and thus plan the basement within the thermal envelope. That is probably also feasible, but how thick the insulation needs to be depends on the energy calculation. And that will (cost-wise) only become clear later (just like excavation etc.).

The advantage of #2 is probably that I could still plan an additional basement room that I could declare as living space (floor heating, windows), for example as a guest room or office.

That is why I tend toward #2. Even if it has a higher cost risk (for example, this requires a more expensive insulating material to include the basement in the thermal envelope) which will only show concrete costs after the energy calculation.

Just forget about KfW40+ and that's it. It doesn't pay off, especially with a basement.

I want to build a KfW40+ prefabricated house with a basement, two full floors, 12m by 8m. In the basement, I have technical equipment as well as a music room, with underfloor heating and connection to controlled residential ventilation. The plot is level. Provider 1 said calculating the basement outside the thermal envelope would be "better and cheaper," so there will be insulation between the basement ceiling and the lower floor, as well as insulation under the music room.

In the described constellation, I see no potential for a choice (except for reconsidering the decision for KfW40+). Provider 1 made it easy for you to finalize with his disqualification, the winner is Provider 2. Making calculations without the host (meaning: consulting the energy consultant, which I consider mandatory at KfW40+, only post alea iacta) would be a homemade April joke straight from the textbook of the Schilda regional kitchen. A music room in a cold basement would be basically equivalent to planning a separate apartment for an instrument tuner. If the plot is really so perfectly level that the terrain does not even have height play of the thickness of the basement ceiling, according to my basement formula you are clearly a no-basement candidate. The floor area ratio would have to be extremely sadistically tight not to build the music room above ground.

Just forget about KfW40+ and that's it. It doesn't pay off, especially with a basement.

As I have mentioned many times before: There are not only commercial reasons to choose to build according to the KfW40+ standard ;)

If it is not the commercial reasons that lead to 40+ with a basement, then the implementation should not be decided commercially either and no lazy compromises like "we insulate a basement room and the ceiling" should be made.

As I have mentioned many times before: There are not only commercial reasons to choose construction according to the KfW40+ standard ;)

But those are the only measurable and, for reasonable people, decisive reasons.
If someone wants to save the world and tell their neighbors how eco-friendly that is, they can do so, but for others, that has no relevance.