Give other matrix clients a try: FluffyChat has separators for DMs, Groups, and Spaces.
Cinny has a Discord look. Mainly a desktop application so it doesn’t have an app, but works fairly well as a PWA.
If you’re on Android, Schildi Chat Next also has a lot of UI/UX tweaks that people enjoy.
Using Stoat's main server raises a privacy concern because it’s UK-based and AFAIK lacks E2EE—UK authorities could seize server data without our knowledge. That effectively means private use requires self-hosting.
Issue with self-hosting Stoat is, it's currently more complicated than Matrix. This user created a detailed GitHub guide that documents their research and pitfalls for getting Stoat working with voice/video: https://github.com/javif89/stoat-selfhost
The official self-hosted guide (https://github.com/stoatchat/self-hosted) looks simple at first, but if you look at the compose file, it requires FOURTEEN containers to run and doesn’t yet include voice/video support which will increase complexity.
By contrast, TeamSpeak’s self-hosting appeal is its simplicity: only two services (or one with SQLite) and it works out of the box today.
But I agree — moving from one closed-source silo to another isn’t ideal. I just wish Stoat were easier to run behind the scenes.
For me, a combination of matrix for text chat and mumble for voice is the simplest and most privacy respecting way to self-host a discord alternative.