You can hide it from other users by using a cloak (which some servers enforce on all connections), if that's a concern (but I don't think it's much of a concern). If you want some anonymity from both the server and users you're probably already connecting to the server from Tor (or maybe a VPN if it's blocked). OTOH discord is difficult/impossible to use from Tor Browser due to phone number requirements on suspicious connections and email verification when changing countries, which sucks.
Yes, and on top of that i don't have to use a javascript enabled browser or some proprietary app, instead i can chose between many minimal and foss irc clients.
Discord is centralized which makes it safer than self hosted solutions
LastPass is centralized, which makes it safer than self-hosted sol.. oh, well, never mind. :-)
Context matters.
Chats/voip when self hosted are more dangerous to its users. I know it from experience.