@fediversereport
I like to think that "Fediverse" follows the same capitalisation rules as "Internet". Both are proper nouns which refer to a inter-network of some sort.
and as with "internet", people write "fediverse" in casual correspondence. that's not to say fedizens (fediverse netizens) believe "fediverse" is lower case, the same way irc users commonly write in lowercase all the time, but they know it's really "IRC", not "irc.
fwiw, I made the Wiktionary entry for "Fediverse".
https://en.wiktionary.org/wiki/Fediverse
But honestly, my mind's not set in stone on this.