Is an inhabited basement part of the thermal envelope or not?

We didn't calculate it because from the beginning it was the only option for us to have everything within the thermal envelope. I estimate the additional costs at 4500 for insulation and 6000 for building services. The base area is 10 x 12 m.

Okay, how did you ultimately insulate the exterior walls of the basement? Did you also use waterproof concrete?

Okay, how did you finally insulate the exterior walls of the basement? Did you also use WU concrete for formwork?

We have water pressure and a slope. Since our architect is a safety fanatic, we have WU concrete + a black tank. Everything is then wrapped with 16cm XPS insulation.

and then consider whether to remove it from the thermal envelope. How much savings is that supposed to bring?

Completely removing it means saving the insulation of the basement enclosing walls, as the ceiling’s insulation only shifts between the basement ceiling and the floor slab. Including the room individually and not the rest of the basement does not work properly or only in naive calculations: properly executed insulation would require "isolation baskets" in the floor slab – which, in my opinion, even in East Frisian jokes only fools would do.

You conduct the heat from the electric oven through the WU concrete (whose U-value I do not know, but it is probably very high) directly outside into the ground.

Correct, just like in millions of uninsulated houses in Germany. Then the oven simply runs at a higher setting and uses more electricity. But that does not matter at all, because you only want to heat the room for a few days a year.

How do you thermally separate the basement then? Insulation on ceilings and walls and separate access or another interior front door. I don't think there's much to save there except in comfort.

As also mentioned, there should be tight and insulated basement stair doors.... so no interior front door is needed.

And insulation on the basement ceiling or ground floor is also logical, yes.

I should practically have both variants costed out. And then it’s a question of money regarding what one decides on. Because a basement inside the thermal envelope is probably more expensive but also more comfortable and maybe more future-proof (if in 20 years a great electricity storage is invented that works worse at low temperatures than at living temperatures). Retrofitting it would hardly be possible.

Although the comparison of electricity costs for the stove in the rather rare yearly case of overnight guests to the additional costs for the basement inside the thermal envelope is probably unnecessary because it will be clear-cut. But as said, comfort and “done is done, because retrofitting is not possible.”

I can't imagine that it's worth not including the basement. In new buildings, it's not unusual to have no heating in the basement, so you won't save anything there.