Mastodon very much supports moving followers/following. Not all others do, but the mechanism is well established. It does not yet support moving posts (it supports exporting them, but there's no import mechanism short of an admin manually doing a database import), but there's nothing that makes adding that technically difficult - it's down to coming to agreement about how to do it.
That Bluesky in theory supports it is pretty irrelevant until they open up federation.
That Bluesky in theory supports it is pretty irrelevant until they open up federation.