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.