You may have noticed this message when sending a DM on StarTrek.website:
What does it mean that "sending private messages are not secure"?
Basically it means that DMs (unlike passwords) are not encrypted before being stored in our database. If I (or the server admin of the sever the person you're DMing) wanted to read DMs, it wouldn't be easy per-se, but it's far from impossible.
Are you reading DMs?
We are not digging through the database to read DMs (we don't care enough to put in the effort also its wrong) but we can't stop other Admins on other instances, and if law enforcement or someone got their hands on our server, there's nothing we could do to prevent your DMs from being accessible to them. Just FYI.
So what's element.io?
Element.io is a secure messaging service that uses the decentralized Matrix protocol. The Lemmy devs like it so much they put a spot in your profile page to make it easy to share your profile:
It's a neat service but has nothing to do with StarTrek.website or Lemmy. It's also far from the only secure messaging platform (Signal and Telegram are two popular ones that allow for it).
Hope that clears up some confusion, feel free to ask any questions! 
Just fyi, while it's possible to have end to end encrypted chats in telegram, they aren't enabled by default.