I personally use both a local password manager (KeepassXC) and a cloud based manager. The “critical credentials” as well as 2fa recovery codes and such go into the local vault. Critical passwords are for example the ones for mail providers, encryption keys for backups etc. which allow me to recover my accounts in an emergency. The rest goes into the cloud manager for convenience.

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I have been told that it is not safe to enable 2FA and use Pass as an authenticator. For Proton account 2FA I am using not only Pass but also KeePassXC as a backup solution (for the case when Pass logout and requires 2FA code in order to login - and in such a case you can not get the 2FA code out of Pass - chicken-egg problem). Yet when using Pass desktop app, maybe logout issue is minimized (it remember my password across reboot and paid Pass is said to work offline).

I wouldn’t … mostly because it discourages you from remembering/memorizing your password, and that’s not something you want to do.

FWIW: I think the local password manager only folks are a bit overly paranoid (and most folks I’ve met of the mindset end up using syncthing or something like that anyways which is basically just Proton Pass with extra steps … so I wouldn’t worry much about that side of it).