Nothing in ActivityPub says you can't move your content from one platform to another. It's just that Mastodon does not have this feature at the moment.
Meanwhile, I'm not sure whether Bluesky has this feature or not, but it's somewhat irrelevant considering the fact that there are no other platforms to move your content to. The only thing I've actually seen from this is that you can use an URL as your username in the front-end, though it just points towards the same DID in the backend. I struggle to see what the great achievement here is.
If this was the reasoning behind Bluesky, they could have developed a platform running on AP supporting the transfer of content between instances, and it would have been a whole lot easier than developing a whole new protocol.