TLDR: The r/selfhosted subreddit has a Discord server. The owner’s account got hacked leaving the server in a precarious state. They submitted a support ticket, but Discord has not taken action in weeks and probably won’t at all, so they are considering starting a new Discord server.
Without having gone on that discord, like most discords, it would be my guess that 80% of the purpose of it is for shitposting, custom emojis, and sharing gifs.
Ironically few if any self hosted chat platforms share that focus, so that’s likely part of the gap. It’s either irc (very light on features, no ui for administration/customization for those not wanting to use admin text commands), matrix (very heavy, focus on federation, also has many commands that are only through text, very light support for custom emoji or built in gifs), or the crippleware open source business oriented chat platforms like rocketchat, mattermost, or zulip.
Honestly zulip is probably best but then you get into the wonderful world of mobile push notifications, capped at 10 users or unlimited for “eligible communities” there
Fluxer recently added self hosting and it has a mobile app in beta and soon to be released, admin from a web GUI, not difficult to host, and has a good amount of discord features. It is somewhat heavy though.