Email requirements for registration are set per-instance. Beyond that, it's my understanding that only a user's existence is shared across instances, in order to attach you to your content. Your registration details stay on the instance you belong to.
Much like reddit, facebook or other apps with dms, only the instance owners (of the instances the users belong to) can see them. They aren't encrypted. There was some work on e2ee messages on the Mastodon side but it stagnated.
if your worried getting spammed with emails, i'd suggest using an email relay in your Lemmy account instead of using your primary email add. Here is an example - https://relay.firefox.com/