I'm gratefull for the comments, though I'm still lost.
It does not help that Fiona's homepage (on pypi) seems out of date (for instance, last test I did on windows, everything went fine with only a "pip install Fiona", including using other packages like rasterstats). Should I raise an issue on Github or do I have it all wrong (I'm still not clear on what is embedded in Fiona wheels) ?
In any case, I'd say that those remarks about building from source when requiring both osgeo and fiona needs to be stated in documentation. I mean by that that people using Fiona are prone to use other packages built on GDAL. (I suspect it also means I can't build a package with poetry if both GDAL and Fiona are required.)
And to sum it up regarding to my first question: so there is no way to change those packages to substitute a Fiona dependency rather than an osgeo call ?