You could also look at Bitwarden. I'm not affiliated, but it's an amazing password manager (desktop app, mobile apps, browser extensions). Even better, it's fully open source; you can even run your own server to keep out a third-party being your (encrypted) sync server. I've been using it for a couple of years now, and have never had a single problem. Free for personal use of almost everything… an upgrade to include the two-factor auth you're looking for is a very cheap $10/year.