Log house in solid wood or post-and-beam construction - experiences?

I would find that great because I consider them to be more environmentally friendly than a reinforced concrete floor slab.
I just need to convince my better half of that

I confused Lucrzia and Johann, that's why I edited.

Are there actually any experiences regarding the radon shielding of wooden cellars and concrete cellars? In some areas of Upper Bavaria, it is quite high?

I also find ground anchors very interesting, but is there already years of experience in (two-story) house construction? I only know them for carports and the like.

I think you are confusing something: the screws under the beam feet are related to rot prevention regarding not standing in water, not with load transfer - they are not and do not replace foundations.

the screws [...] are not and do not replace foundations.

On Gesundbau's homepage, the ground anchors explicitly are presented as a replacement for the concrete slab.
I also received a cost estimate from the provider Rast und Ruh, stating that the house will be built on 30 of these ground anchors.

I would like to link accordingly, but unfortunately I am not allowed.
However, it can be quickly found via Google.

On Gesundbau's homepage, the ground anchors explicitly are presented as a replacement for the concrete floor slab.

Correct. But

I only know them for carports and the like.

points out that is basically lumping the screws between the ground and the carport support beam ends together with ground anchors.

has a wooden cellar. I just don’t know how the floor slab is designed.

The floor slab is also solid wood. Unfortunately, I don’t have a picture, but you can check out the photo gallery of the "Haus am Hang" on the website of the Staudenschreiner (google it - you’ll find it immediately), there you can see it.