Floor structure with uninsulated base plate

I read indications of the desire to build very ecologically...

I read hints of the desire to build very ecologically...

In that regard, I can understand the OP. We wanted that too, but you have to make compromises. For my floor structure, it was mineral wool in the end. I could certainly have used wood fiber insulation boards like on the walls and roof, but here the flexibility of the material spoke for itself (we have all kinds of lines like controlled residential ventilation, water, electricity, etc. in the floor). So: I have my floor structure almost exactly as the OP outlined it. However, we have waterproof concrete as the slab, insulated underneath with 12cm XPS, and the entire slab was fully sealed on top; our shell builder insisted on that. Maybe one more recommendation: If you're already using cross battens, then insulate crosswise in two layers to avoid thermal bridges.

As far as the floor construction is concerned, it looks pretty much exactly like in your sketch. However, we do not have a moisture-variable vapor barrier. Our waterproofing of the floor slab consists of welded bitumen sheets. I cannot remember a dimpled membrane as a clean layer.

I am also happy to share pictures of my construction again ...

Bitumen on the 30cm BP, the cross battens fixed with brackets on rubber granulate pads, mineral wool in between. Then a "soft" thin OSB, impact sound insulation made from castor oil (organic), and on top of that smoked oak wood parquet.

I am also happy to share pictures of my setup again ...

Are the beams in the floor cantilevered over such a large span?

Are the beams in the floor spanning freely over such a large distance?

No, of course not. There are hardwood blocks + rubber granulate at shorter intervals, also heavy-duty brackets with rubber granulate for cushioning to fix them.
The lower beams (max. 7.1m long) are also decoupled from the wall with rubber granulate. Cross-sections of nearly 100cm height would probably have been required there.