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

What interests me more is the mixed calculation in case a basement exists.

How would it behave if you already have a hole from the demolished existing house?

A specialist must or should calculate for you how expensive it would be for you. Whether the existing basement is still load-bearing, whether it can be extended to a comfortable height.

But does this mean that in the case of a (pot) flat plot, you would never build a basement, right?

There are mini plots, there are families with 3-4 children, there are restrictive development plans, there are side businesses, where a basement would be worthwhile in each case, even if the plot is very flat.

And a hobby does not have to be rational.

But the hobby must be affordable. If a horse lady comes along with a special plot and wants to keep the horse on her property, but overall the project is not financially viable, then Plan B should be considered. If a photographer wants to call a light-flooded studio her own, it might not fit the budget.
And the dream of a mechanic's or carpenter's workshop might also not really fit in the basement.
A workshop can be very well integrated into a shed in an old development plan, which is usually much more practical on ground level if the material or product is somewhat bulky.

A 10m² storage fills up quickly with skis, suitcases, hiking boots, jars of jam, and (currently) raclette and Christmas tree decorations.

Usually you still have the attic, which automatically arises in a gable roof house. That is why I almost always recommend this option rather than a city villa, which offers no flexible storage space at all. Side areas are suitable for skis and suitcases, and you can chop them off.
Ultimately, however, much is shaped by finances. A basement costs, just like waterproofing and the like in problematic soil conditions.
Then comes the nice-to-have demand.
However, there are of course alternatives: anyone who still really wants a pantry and a mega dressing room also has storage space here. A storage room should be able to house common utensils on the ground floor anyway, despite the basement. And laundry can also be washed very well on the sleeping floor if the floor allows for it space-wise.
Personally, if I could, I would always decide on a shed or storage room in the garden. You need it anyway for lawnmowers and bicycles. And I also prefer living space with daylight quality.

What now somewhat concerns me is the cellar question. Of course, I have already read the 11ant cellar rule. But I think I don't understand it.

Before I answer you (certainly not tonight), you can already draw the existing condition on the property and comment on how the intersection of the old and new house floor area would turn out.

Good morning, first of all, I wish you all a healthy and successful year 2025. Attached is a sketch: Blue is the current old stock. Garage top 6x8 - presumably not basemented Haupthaus (I think 9x9 or 10x10) - low basement, condition somewhat appropriate for the age. Extension east plan right (8x5) - the basement is about 40cm lower, but some kind of mistake was made there. It is damp and moldy. And the basement ceiling/ground floor floor is cold. The new building 7x11 would almost exactly overlap plan top/plan left with the existing building. This gives a) the building line plan left and we want to be as far north as possible to have more garden area in the south. To the north, the building boundary with 6m = garage width is given. Over the entire length of the south facade (18m), I would estimate the height difference to be 0.5-0.8m, sloping down towards the street. Only in the garden west between the street and the building is the height difference another 0.5-1m. At the street, the garden is about 0.5m terraced with a small concrete wall/L-blocks. That means the driveway to the garage has a good 1m height difference. Best regards

Whether the existing basement is still load-bearing, whether it can be built up to a comfortable height.

That would be an important sticking point for me. Do the old walls carry your planned new house on top? It is not uncommon to plan higher, bigger, further than before. Then the structural engineering can already answer the question with "get rid of it." Otherwise, poorly usable rooms due to lack of height quickly end up on my chopping list when the excavator is already there. This disadvantage is basically never compensated for and does not make you happy. If I understood correctly, the current basement wall heights cannot sensibly be raised further either, as the whole thing would otherwise become a high-rise. Based on the current knowledge, I am clearly on the side of "tear everything down and start anew." The new build costs a small fortune, which one is reluctant to throw away on patched-on and questionable compromises.

Thank you very much for the specific feedback.
That was very important to me, even though I already had this tendency.
However, I also had in mind that the "tear everything down and start anew" attitude sometimes goes too far.
That’s why I wanted to ask again.
Renovating the existing building was once an option. But since the layout is very unfavorable and there is no high emotional value attached to it,
we have filed this away.

Then I would like to come to the follow-up question.
Demolish and build a new basement or level the ground and build bigger instead?

Today we roughly estimated our space requirements based on the apartments/objects/experiences of how we have lived so far.
(Or how others perceive it)
In the basement, we came up with the following areas:
14m² for technical equipment + laundry
20m² for the hobby workshop
8m² for storage
18m² for guests/office

In other words, 1/3 residential basement and 2/3 utility basement.
(Unless I manage to convince my wife to equip the workshop with underfloor heating too. But I don’t need flush-mounted electricals, fine plaster, or marble tiles there either)

Of course, I would also accept a 20m² garden shed as a workshop. But having it separately with its own roof and sufficiently insulated seems about as expensive as putting it in the basement.
(Therefore, once again the request to disregard the usefulness of a 20m² workshop outside)

I also wish a happy new year with much joy in building your house.

It is damp and moldy. And the basement ceiling/ground floor floor is cold.

Then it can and should be removed.

"remove everything and redo."

Exactly!

That is a) dictated by the building line on the left side

Is it actually a building line? Does the neighbor at the bottom of the plan have a different one? The house is closer to the street after all.
I would probably, since the property is big enough, do without a basement.
Whether or why a basement is necessary is currently discussed here in the thread incidentally
https://www.hausbau-forum.de/threads/grundriss-hausanordnung-efw-150m2-keller-einliegerwohnung-feedback-erwuenscht.48571/page-11#post-678863

And I would not downplay the importance of the west side if you have the possibility to use it.
How to deal with the slope, that needs to be seen. You can model 80cm by terraces and shrubs.