Medium Beta is one of the oldest beta programs around. Medium beta testing community existed in Google+ in 2014 when many popular apps didn't even think about having a beta release track.
Many things changed since then - Google+ doesn't exist anymore, Medium got a new logo and app design. If I remember it correctly, the community on Google+ had around 10k ppl in total. The same as many other beta testing communities on Google+, Medium community had to be migrated somewhere and they decided to go with a Reddit community as an alternative to Google+.
Medium beta community on Reddit: https://www.reddit.com/r/MediumApp/