Matrix? It's also quite close and federated as well.
There's Revolt that seems to be very similar to Discord. They even have instructions to self host on their github repo. Don't know if this matters, but as of right now it is not federated.
Matrix
Linen (https://linen.dev) can sync Discord chat, it doesn't have voice or video capabilities though but at least backs up the important content.
The worst part about Discord is how nothing is indexed by search engines, so when you need help with something your only option is to join a Discord server and ask for help, or use the crappy search functionality.
I’ve seen Linen before, but haven’t found a community that actually uses it. It would be great to see it (or a similar alternative) take off in the software development world, where this type of thing is probably most impactful.
Edit: for a casual or private chat room, Matrix is probably better though
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