Insulate floor slab - ceiling height is not sufficient

Once again for understanding: The house currently has no basement? Perhaps there is a filled-in basement and concrete was probably just poured over it?

That already reads strangely. Some rooms have basements, others do not, and then there is a concrete floor in a half-timbered house. What is the year of construction? Our house is fully basemented and at some point, screed was poured over the natural floor of the basement and then tiled. Also not a good solution, but that's how it is now. In old buildings and especially in half-timbered houses, it is better to stick to what has proven itself over centuries. And I would definitely want to have the question of the basement clarified. That is important information.

The old house also had only a partial basement. At some point, an extension was added and the area was filled with soil and rolled gravel. Concrete on top, done.