Termination of basement construction contract - experiences?

These are the formulations from which we did NOT conclude that the house building company is supposed to do the workshop planning for the basement

The architect is the house builder’s, commissioned additionally by us only to co-draw the basement for the building application.

Why should a heating system not be outside the thermal envelope? The hot water tank and pipes are insulated after all, and the basement itself is also insulated. What is the difference to your variant B?

The basement is insulated, just (officially) not heated. In fact, we want to later accommodate a hobby room/guest room in the "workshop" and also provide heating for cold days, as well as for the adjoining bathroom.

Only the basement builder is truly qualified in this game to do the detailed planning for the basement. It would be easier for a camel to go through the eye of a needle than for the basement builder to have trained the house provider on their system. It would have been better if the architect hadn’t stood "on the sidelines", but had been the "mistress of the process" you commissioned, all planning would have been done by her, and you would have awarded the basement through the house provider. I have been involved in construction topics for over forty years and would not order a basement separately. The fact that the basement builder needs documents from the house provider here does not mean that the house provider would or could deliver the basement execution planning.

This is practically your core problem: The basement builder needs the cooperation of the house provider to fulfill his necessary preliminary services – so much for "apart from communication, he has done nothing yet". No, he CAN’T do it that way. If I were a judge and had to settle the dispute, I would clearly see the basement builder as the injured party and fully consider his claim to compensation with drums and trumpets as rightful. The situation becomes truly tricky because you are also the ones responsible for providing the cooperation of the house provider in the preliminary services of the house builder for the basement construction. With hopes for support or mediation, you are at the architect’s address farthest off ever. Expect your lawyer to even advise you not to haggle over the basement builder’s contractual damages by a jot. And let the lawyer solve the problem. It’s a pity that you’re in NI, in RP I would have recommended Mrs. Reibold-Rolinger to you.

Ouch.
Theoretically, I have already answered your question about the difference, but practically it is irrelevant here anyway (since I can at least gather from the poorly legible drawings that the basement is not outside the thermal envelope here. Rather, your problem is that you want to exclude rooms within the thermal envelope (for which the location on which floor is irrelevant) from the heating load calculation. Don’t take it personally, but may God keep such squarely clumsy clients away from me in my construction consulting, you can hardly manage to behave more stupidly. Once again, I understand the basement builder (and honestly, if I were in his place, I would even turn the tables and offer you a golden handshake to terminate the contract).

Nothing more to add to that, the question is how the original poster will now deal with it?

I hope that the problems also simply stem from the fact that as a layperson I always have to pass on information and requirements (Chinese whispers principle) and that simply cannot work.

The basement will be insulated, but (officially) not heated. In fact, we want to later accommodate a hobby room/guest room in the "workshop" and also equip it with a heater for cold days, as well as the adjoining bathroom.