Is the offer for liquid screed and laying tack boards too expensive?

Well, if the base slab was supposed to be 12cm thick back then, but at some points only measures 7cm (assuming that the areas where a lot of screed had to be applied were poured too thinly), that is a defect where one would have to say for new construction: remove everything and do it again. The rebar must lie correctly in the concrete. But in an old building, you have no idea how it was built. So you can’t really worry about it much.

So rather expect increased moisture ingress. Then better no anhydrite screed.

For example, with (bound) bulk fill. Leveling compound will exceed your budget and the differences are also too great for that.

Is there really still increased moisture to be expected?

So far it was a utility basement, now it is being converted into a living basement.
Year of construction 1963
The house stands on a strip foundation and the ground is filled with rammed concrete.
What problems should there be with the thickness of the ground?

You have a completely wrong idea. But you are well advised

You have a completely wrong idea. But you are well advised by the construction consultant .

However, if you only have a strip foundation in the basement, you can assume that it is only partially protected against rising damp. So far, the rammed concrete has regulated the moisture in the basement. If you now seal it off with foil, the moisture will then be drawn up through the foundation into the walls. The moisture barrier is usually no longer the best in buildings from that era.

If you also have anhydrite in the floor, it will rot in a very short time. As I said, with your new structure you will disrupt the entire moisture behavior of the masonry. I would proceed very carefully.

First, I would clarify to what extent the barrier sheet in the wall, i.e. from the foundation to the wall, is intact. In the 60s, roofing felt was usually used, which dissolves over time.

So you don’t want to finish everything nicely with underfloor heating and screed and the like only to have to have a new horizontal barrier injected by a specialist at great expense later. You wouldn’t be the first.