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

And: The larger the enclosed space (volume), the easier (in principle/calculatively) it is to meet KfW requirements regarding primary energy consumption in kWh per m²

How does Anbieter1 want to handle the edge insulation created by the stairs and so on? Simply leave it out?
You can achieve a pure building energy law with a heat pump and a thermal bridge surcharge of 1.0, at least according to the old expiring DIN. But with the KfW, that won't work.

How is Anbieter1 going to handle the stair and the resulting edge insulation?

Anbieter 1 informed me as follows:

Frame/sill elevation for raised floor construction
a thermally insulated interior door
an interior staircase with risers
reinforced and thermally insulated interior wall under and next to the stairs
insulation increased to 180 mm under the underfloor heating instead of the 140 mm load-bearing insulation under the basement slab.
The basement does have living spaces but is still counted as outside the thermal envelope - it is the better and more cost-effective option.

They also have a KfW55 basement within the thermal envelope, but they think it makes less sense for KfW40.

An independent basement builder told me:

We very rarely have a basement as KFW 4[0] that is not part of the envelope.
Also, if you have the technical equipment in the basement, it must be inside the thermal envelope!
I cannot confirm insulation of 120-140 for KFW 40, not with either house manufacturer!
But your consultant knows exactly what insulation you need with your equipment for KFW 40.
We have no influence on the insulation; this is always specified by the house manufacturer!

The basement builder says the basement must be inside the thermal envelope because I have equipment in the basement. This contradicts Anbieter 1.

I believe the 120-140 perimeter insulation is sufficient for KfW55, as it is also offered by Anbieter 1 for KfW55 basements. Unfortunately, no information is given for KfW40...

Depends on many things, but in my opinion you can forget 140 mm easily. The target for Kfw 40 is (very roughly simplified) for basement walls and floor slab a U-value smaller than approx. 0.19, which is only achievable with WU concrete 28 cm combined with XPS insulation at 180 mm or 200 mm perimeter insulation. What of course also works is core insulation made of PUR/PIR between element walls plus XPS on the outside, then the total thickness can be a bit thinner.

Okay, then Anbieter1 has certainly given some thought to their offer. What is important here are the thermal bridges and less the insulation thicknesses. The KfW also points out the costs in this regard. Because over-insulating the surfaces is often more expensive and does not serve to prevent possible building damage.

Ultimately, both providers must provide proof. The crucial point here is how the thermal bridge surcharge is proven. For this purpose, the KfW provides 3 methods. Precisely speaking, only then can the concepts/the specifications and the costs be compared.

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Oh, and according to which standard the calculation was made, preferably according to DIN18599 with the new supplement 2 and not the outdated DIN 4108 with DIN 4701-10, which allows for easy "window-dressing".

Kellerbauer meint dass Keller in Thermischer Hülle sein muss, da ich Technik im Keller habe.

Correct, WP MUST be within the thermal envelope. So you still need a technical room above ground.