I just queried #Wikidata how many institutes and universities have Mastodon account, and seems most of them are in Germany (103). We need to thank the @neuSoM effort to convince universities to migrate from Twitter to #Mastodon.
However, I don't find how to query how many institutes hare integrated with the Fediverse beyond Mastodon. For example, the CS department where I studied has a #PeerTube channel (https://pt.dcc.uchile.cl).