Edit:
I reached out to Lemmy World admins (!lwadmin) and they said:
If a user is banned on their home instance then it federates to others, if banned on instances other than their home, it doesn’t
As far as I understand;
A user is specific to one instance. In order to interact with the fediverse on that specific account, they need to log into that instance. If they’re banned from that instance, they cannot log in and interact with the rest of the fediverse.
There’s nothing stopping them from logging into an alt, whether on that same instance or on another instance.
I am not an expert, only a user, so take my remark with a grain of salt.
To my knowledge a banned account is only banned on the instance that bans the account. Federated instances would not automatically ban the account unless they have a bot or some similar function specifically for that.
Obviously, automatic federated banning would be a huge, massive problem for Lemmy. If a small, tiny instance decided to start banning accounts for whatever reason, the accounts being automatically banned on all federated instances would be a major design flaw since instances start off as automatically federated.