Rebuild the floor from scratch

I have no problem with the ceiling height, it was 2.70 m and now it is 2.90 - 3.00 m. I have now also removed everything in the bathroom. The neighbor, about 80 years old, said yesterday that the clay was not filled in, but that we are on clay soil. This means that there is clay soil everywhere. So I don't have to worry about the thickness. I have seen that a foam glass company advertises that foam glass gravel replaces the concrete floor, the clean layer, and drainage, and also provides some insulation. But who has experience with it? Apparently, only a fleece has to be laid under the screed.

that the clay was not filled in, but that we are on clay soil.

Yes and no. A rammed earth floor can certainly have been made with the clay already found on site, but probably still compacted layer by layer. Just not brought in separately first. Where the existing composition was suitable, conceivable and practical.

I have no problem with the ceiling height,

and with the lintel heights?

I saw that a glass foam company advertises that glass foam gravel replaces the concrete floor, the clean layer, and drainage and provides some insulation. But who has experience with it? Apparently, a fleece just needs to be laid under the screed.

I have not dealt with this yet. The fleece is probably supposed to prevent the screed from flowing around the glass foam granules, encapsulating them and thus forming a layer with them. Sounds logical to me.

The XPS boards can support the weight of the floor but they must lie absolutely flat. There should be a leveling layer, which should also be firmly bonded in the installed state. At least this part, I would have done by a professional company. How is it now prevented that moisture rises into the walls from below if the whole thing stands purely on clay soil, setting aside the load-bearing capacity of clay?

Depending on how many additional cm are added, the lintel would not need to be changed or at most 1 door lintel. XPS would be an alternative but I am missing the substructure. The walls still need to be horizontally braced. The floor slab in the kitchen had damage, presumably due to moisture, and there was bitumen under the screed in the bathroom. The clay seems to bear well, at least for the last 126 years. The basemented part only became wet when the city removed the clay and filled it with sand.

How is it now prevented that moisture from below soaks into the walls when the whole thing is standing purely on clay soil, aside from the load-bearing capacity of clay?

Wow, I used to think biologists were natural scientists. Clay is a top-notch moisture regulator – it's precisely because of the clay that the climate inside the box is stable. The load-bearing capacity after tamping is excellent; the stuff becomes as solid as dry gray bread. Typically, rammed clay and rammed concrete are combined in a way that fits optimally. This is slowly making a comeback. Construction is also a cultural technique.

I also studied geology - a biologist actually knows nothing about clay. A geologist does. For example, that clay, i.e. clay/silt, forms water-impermeable layers and can never become completely dry (adhesion water). When wet, it tends to flow plastically; on inclined layers - no idea how it looks with the OP now - it may then lead to slipping of the layers. Practically everything depends on how dry the whole thing is (but it never gets completely dry see above), how the layers are arranged, and how the moisture input looks like, for example during heavy rain. Even the driest clay is "relatively" wet. Regarding load-bearing capacity, that is not necessarily the floor filling but rather what the house stands on, the question is therefore justified after all.