I'm a little late to this, but I feel the need to mention it because I feel like these people are just going to move to Telegram, if they already haven't.
Telegram is NOT a better alternative to Discord. It asks for your phone number (huge red flag), lies about being end-to-end encrypted (encryption is done server-side), is centralized, and not entirely FOSS (server-side software is closed source). Look into decentralized/self-hosted solutions instead.
I personally recommend hosting an XMPP server. Install an XMPP server stack that supports multi-user-chats and host your discussions there. With XMPP, you can sign up for an account on any server and talk to anyone, including people from other servers. There are even modernized web-clients like Movim which make it more user friendly.
For private/direct messages, you can also end-to-end encrypt them using OMEMO. Just don't use them for public MUCs or you will end up having problems. You really don't need to encrypt a public chat anyway.
If you need help running an XMPP server, Mental Outlaw made a video on it.