This turned out to be the problem. After updating python I ended up with python 3.9.*. Downgrading to python 3.8.* made it possible to install the wheel.
Unfortunately I still wasn't able to run python -m prodigy stats: it kept returning missing module errors. I ended up manually installing a whole bunch of them (murmurhash, numpy, blis, pytorch, thinc etc.). After doing all of that I was still getting an error message:
ImportError: cannot import name 'wrap' from 'thinc.api'
I kind of ran out of inspiration at that point. Since installing all those seperate modules was turning my site-packages into a mess, I decided to create a new conda environment. This completely solved the problem. I was able to run python -m prodigy stats.
The conda environment that was causing all the problems did have spacy (and all its dependencies) installed. I'm guessing there was some kind of version/dependency mismatch going on?