think of how you can set up an auto-forwarder in email. it isn’t expected to be your address forever, but people eventually figure out that you’ve moved to a new address when you reply to them from that address.
so the “soft” version of a migration is to show a banner that you’re currently at a new account, but anyone replying or mentioning that old account will not be seen at the new account unless you actively go and check your old notifs or threads. (an auto-forwarder would help fix this.)
the next level after that is to notify your contacts (followers, etc, anyone you want really) with a migration notice, currently done via a special Move activity defined by Mastodon (which is kind of weird semantically, and it can be inconsistent between softwares as mentioned above, so it would possibly need some standardization).
upon receipt of whatever activity, your software has a choice to either generate a notification (as in pleroma), or perhaps auto-follow the new account (as in mastodon, which also force-unfollows the old account so you lose access to old followers-only statuses, which is actually pretty bad when you think about it, but no one really thought about it since 2018)