This is sadly not quite correct. You can send out a 'Move' activity from your old account, notifying other servers that you have moved. There's no guarantee that they understand that activity, or, if they understand it, that they actually follow the new account automatically.
In practice, nearly all your followers will be using fediverse software that understands and supports Move{Actor} in a similar way to Mastodon. There's not a massive amount of fediverse software - it's not like IndieWeb where everyone does their own thing - and the microblogging-focused software largely implements the same feature set.
That depends on that software being deployed in a timely manner. There's plenty of instances out there still on Mastodon 1.6 and 2.0 because the admin installed it 2 years ago and hasn't updated since.
I probably need to look into supporting this in my federated social network thing. It does work with Mastodon and Pleroma right now, but it certainly could do better.
Even if the move notification worked perfectly, the people on instances your local admin has defederated with will never receive it as a result of the defederation. I don’t think this is a solution.