Earlier quoted context omitted.
Zulip isn't a Matrix server. Zulip doesn't federate. If you want a private, non-federated chat server -- for your organization, basically -- Zulip is awesome. If you want federated chat, Zulip doesn't do that.
Since every matrix server requires you create its own user id, I never understood the benefit of being federated.
you can use a mozilla.com user id to talk to someone with a matrix.org user id, or a kde.org user id
all servers are equal participants in rooms, so a room doesn't live on a specific server aside from servers being able to create friendly names pointing to them, but nothing stops #foo:kde.org from pointing to the exact same room as #bar:mozilla.org -- both servers are participating equally and have their own shortcut name to the room