I host a Mattermost server for this purpose. It does what Discord does, just shittier, buggier, fewer features, and I have to pay a web host to have somewhere to run it. But it's -actually- private and our community owns the data, instead of whoever buys Discord next week.

I wish there were more self-hosting offerings to compete with Discord. RocketChat, Mattermost, Zulip, and Matrix/Element all leave something to be desired.