More progress! Well, I have no idea the details but in short, the yellow things you see in the photos are the base of the support for the basement ceiling. Unlike in US where, from my experience the floor is framed with wood and plywood, the floor here will be made from concrete. This is totally normal in Europe and part of why the houses here are so quiet…much less reliance on sound-proofing from wood frames and drywall and rather solid brick floors and walls.
You can also see that more insulation and waterproofing is going up on the outside of the basement walls.
Either way, we should see a basement ceiling this week and in one month the actual house itself should start going up.