Everything is running fine. It is as @jon@jon@lemmy.tf and @neoney@lemmy.neoney.dev write.
If I am server A, and I federate with B. If user@B is banned by B, this is propagated to me, so that A does not see content from B that comes from user@B. It makes sense.
Given that I asked the question in the first place, here is how I make sense of it after some answers and looking at the modlog.
Because A sees B's content, but on A server. user@B is banned on B, hence, A keeps seeing B content, but not user@B content on B. user@B can still register on A and post there.
Because user@B's content, while copied and displayed on A, is still B's content. B bans the user and their content everywhere. Again, user@B can register elsewhere and start posting.
From what I can see, if I am A, I cannot unban user@B in any way. user@B can register in my instance, though. I can ban user@A afterwards (or not).
I think so. I federate with Beehaw. If Beehaw bans everyone, my banned user list will get quite long.