I have been using Wire only for my real life friends and family for the past 2 years or so now.
It is open source, but their server isn’t clear, they said they would make it fully open but I’m not sure where it’s at currently.
It may be fully open, but if you run your own server it doesn’t federate with the primary public Wire server.
It does pretty much everything, except mass group chats (there are no public groups, you have to be invited by someone)
Group voice, video, screensharing is limited to 5 people at a time in the free version.
They seem to have really been pushing their enterprise version, which is slightly worrying as people assume someday they will just kill the free version.
Bringing me to the Matrix network (the most popular client being “Element messenger” and what most people probably mistake as the entire network)
Matrix is the answer to OP’s question.
The server and clients are fully FOSS, anyone’s server federates with all others (though most people end up creating an account on matrix.org)
1-to-1 conversations, voice/video calls and all media sent are default end to end encrypted.
new rooms created still let you decide weather they are end to end encrypted from the start or not.
But you can make a new room public so anyone can find through the search, and you can have it all end to end encrypted by default if you choose.
Group voice/video is currently done through integrated ‘Jitsi’ systems. (Jitsi being a very good near equivalent to Zoom)
You can turn on encryption for group voice/video calls, but they are working hard to make everything fully end to end encrypted by default as soon as they can.
To cut it short, Element messenger is trying to do almost everything the mainstream big names are doing (Discord, Zoom, Slack) except fully FOSS and fully end to end encrypted (soon enough)
No need for phone numbers, and you can use it from a browser without installing anything if you want.
Edit: I forgot to include that either the Matrix team or the Element team, are working on a way to run the clients fully P2P, that’s all I’ll note because I haven’t looked into the specifics of it. But this would bring Element messenger in league with the fully P2P messengers like Tox, Briar, Jami.