I'm an academic. Since the pandemic began I've used Discord on multiple occasions for work -- for example, if someone runs an online conference it's common to create a Discord and encourage chat among the conference participants.
But these are all fairly informal use cases, initiated by individual academics and not by "the university".
If you ask university IT about Discord, they'll probably tell you emailing .docx files back and forth is just as good.
My university's IT staff is surprisingly good. But they seem to be hamstrung by questionable decisions being made over their head.
To be honest, I’m not that in touch with enterprise. Despite Discord’s appearance as a platform for gamers it has pretty much dominated slack for a non-self hosted solution for the areas I’m familiar with. Small teams, OSS, cryptocurrency, strongly distributed WFH type startups, conferences, etc. Private channels are role based so the general public can integrate communication tightly with the main team while they work behind the scenes. I wouldn’t be surprised if Discord launches a professional de-gamer-branded version soon. Target markets aside you simply get more from Discord for most general use cases and it feels like Slack is playing catch up rather than leading (like they used to) on some popular features.
Also, Discord has capable APIs and a fairly open developer program. You can make some really amazing and useful bots.