Correct, a new account since accounts are tied to the instance. It's not a great experience at the moment but I suppose part of the trade-off for now with the fediverse. Maybe a tool or something native will be made later to help the use case.

Your username is made on instances. So yeah, you can't just switch. However you could just recreate the username on a different instance though.

You have to have a separate account for each instance. That's how Lemmy and other federated sites work. That's the whole point.