Revolt is the most Discord-like FOSS chat app; it's very easy to use and customizable. Rocket.chat and Mattermost do similar things and are more oriented toward organizations (the Slack/Teams Classic use case).
I second revolt Been using it for a few months now, it really feels like Discord
A Matrix server with a nice web based client, hosted on premise. People are then free to choose the mobile or desktop apps they want.
Matrix is missing the entire voice chat, video chat, and streaming aspect of Discord.
It has meetings and calls, but those are much less convenient to use compared to persistent voice channels, and the streaming had a lot of latency when I tried it last.
Mattermost, it might not be the best feature-wise, but it's open source, and a university can host it's own server with SSO
Matrix / element with the jitsi voice rooms, has Discovery just like discord. You can see that people are talking in a room, and you can join the room and join the conversation. You don't have to click on to a voice room with nobody in it.
slack for teacher to teacher mabye
I don't have experience using it, but it is worth looking at BigBlueButton.
Nextcloud Talk on school's private instance
