Existing basement or new full basement, or no basement at all?

That is to say 1/3 residential basement and 2/3 utility basement.
(Unless I manage to convince my wife to have the workshop equipped with underfloor heating as well. But I don't need flush-mounted electrical installations, fine plaster, and marble tiles there either)

Well, simply dividing it like that to save costs isn't feasible anymore.
The gentle slope doesn’t call for a basement (as already mentioned above), ultimately it’s all a matter of budget.
How much budget is available?

https://www.hausbau-forum.de/threads/interpretation-bebauungsplan-von-1957-moeglichkeiten-fuer-neubau.41078/ For anyone interested or if there are further questions about the development plan etc., one should link the old threads, at least this one. You could have also connected to the thread. Whatever. Did you manage to clarify all questions with the building authority back then?

I would of course also take a garden shed with 20m² as a workshop.

I don't know your hobby, but do you even get the machines down to the basement and then the workpieces back out again? How loud is the whole thing? With underfloor heating, how heavy are the machines?

I would of course also take a garden shed with 20m² as a workshop. But seeing it separate with its own roof and sufficiently heat-insulated, I currently see it as expensive as relocating it to the basement.

Such a garden house with 44mm wall thickness all in should cost around 6k with foundation/slab. Whether you absolutely have to insulate it, you have to decide yourself. It can also be heated well enough if you are not inside constantly every day. But in the basement it will also only be 12-14 degrees without heating (if a usable basement).

For that price, otherwise, you only get the planning for the basement.

Here are two screenshots of the development plan. Indeed, that is the building line and it is also true that the neighbor is positioned offset, closer to the street.

I had mentioned the 1/3 residential basement to 2/3 utility basement not to get a mixed calculation, but for the estimation for the question: "Basement area shifted above ground level." With 100% utility basement, this question would certainly be answered differently than with 100% residential basement. Or?

Indeed, the plot is large enough. And the development plan also provides sufficient buildable area. I was only concerned with the question of how it behaves when there is already a hole there, since the existing basement has to be removed anyway. To what extent a house without a basement is cheaper or more expensive than a house with a basement. If the areas are identical in both cases.

To what extent a house without a basement is cheaper or more expensive than a house with a basement. If the areas are identical in both cases.

You have already received the answer here often enough. Asking more often doesn't change anything.