Yeah it’s all federated. If you get banned from a community on Lemmy.world, you will not be able to access it from Lemmy.today for example (with your lemmy.today user account).
This is the really super cool part about the fediverse. People don’t realize… This is where the magic is.
If Lemmy.world is down, you still access posts and threads and make posts etc from lemmy.today… And it all syncs when Lemmy.world is up again.
Another mind blowing moment is when you realize you can read and post on Lemmy from Mastadon… So you can combine interacting with Mastadon and Lemmy in the same conversion.