They are not that secretive, it's been written about several times. Long story short: a lot of it is still Glenn McDonald, the person behind everynoise, that was acquihired when they bought echonest.
Here are a few articles about it (there are several more): https://artists.spotify.com/blog/how-spotify-discovers-the-g... https://www.thefader.com/2020/12/02/escape-room-genre-spotif... https://www.thestar.com/entertainment/2016/01/14/meet-the-ma...
Well, ideally your spotify artist page should contain the genres you're tagged with, along with some info of how that came to be, and even a way to request a change to those. But they don't want people to game the system, and also not let competitors know how they do things (I'm guessing).
At least you get the genre info is in the web API, just not present on the artist page (you need a token for the query to work, but you can create that on dev page):
https://developer.spotify.com/console/get-artist/?id=10YNQq8...
But nowadays I'm guessing they are utilizing their huge dataset of playlists to group artists under tags. Obviously such systems will work better the more popular an artist is.