> but I am using Bitwarden free and there's no authenticator app
There is if you pay $10 annually for Bitwarden Pro.
I use it, and it was the game changer I needed in terms of user-experience, to bother actually start using 2FA/MFA for all sites where it was an option (compared to before where I would only do it if required).
They haven’t had the feature for a huge amount of time but it works alright, with some minor mistakes here and there. As with most managers, it struggles when there are more than two fields to populate