Yes "identity" is per server.

>So your followers on one server are not able to follow you on the other using the same credentials.

You misunderstand. Of course they do. You can talk to any server. This part is called federation. Admins can defederate other instances or individual users though. Well the point here is that you find suitable server. On Nostr relays can do the SAME and you must equaly find suitable relays. So the relays are instances. There is no fundamental difference. People not using free speech relays won't be able to find you. This will be majority of users who use defaults. The users using default normie relays will not touch free speech relays. What's the difference? Nothing. And this will yet go further as blocklists Nostr devs and relay operators discuss will be implemented. The free speech portion of Nostr will be one digit % and liberals create their Berlin communist wall again. You can't stop that with any protocol. We can only argue nostr makes it slightly easier as on fedi you need to create new identiry here you just switch relay, if there is such.

From a fedi admin friend:

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