So far, I've only found clients with different bugs. Calling them good would be a stretch. Passable, perhaps. But the scene as a whole is more of a choose-the-bugs-to-live-with situation than choose-a-good-client.
Welcome to Matrix. It's the best option there is, and it's not very good.
I've never thought of matrix as a mature technology ever since.
even mastodon figured out federation.
It sounds like you were trying to login to Mozilla's Element web client and it was only set up to authenticate against the Mozilla homeserver but A) that's a client setting unrelated to federation or really the protocol in general and B) not what you were supposed to be doing to begin with.