Price difference between ground slab and basement. Can it be estimated?

Thank you for the answers! We will simply see what other construction companies say, plan, and see what comes of it

renting an apartment nearby is our Plan B
it has to be a self-contained living unit.

It is questionable in my opinion whether a separate apartment ([Einliegerwohnung]) is the right option at all for someone who is no longer independent. If one goes through with it, this apartment must be suitable for care (sanitary area, door clearance widths, etc.; possibly a guest area for care personnel).

So that our mother/mother-in-law will not have to live alone in the foreseeable future, I don't think she is already in need of care. She lives 150 km away from us and has some ailments. Cleaning, shopping, cooking, etc. are becoming increasingly difficult for her... additionally, due to an eye disease, driving is already borderline for her and it will probably worsen to the point where she will no longer be able/allowed to drive. However, she lives in such a rural area that NOTHING works without a car! These are, among other things, the reasons why she is moving in with us. And if care needs should arise, we want to have her with us as well. With outpatient nursing services, care-dependent people can almost always be cared for at home, especially if relatives are nearby. Doors and bathroom will be planned accordingly. The staircase to the granny flat could have been managed if necessary... By the way, we have now had an appointment with another general contractor. They say that an extension is not really more expensive when all costs are considered. So it will probably be an extension.