I also use Authy, so I want to point out something. Authy doesnt exactly "store the credentials online"; they do allow you to store an encrypted snapshot backup in the cloud which you can restore from, but that's not the same as storing them in the cloud.

As far as I can tell, for cases where you're just using Authy in the same way as Google Authenticator (a big standard TOTP app), the only value proposition is that Authy allows separate programs with your TOTP keys in them to communicate together so that they all have copies of the same keys. It seems in those cases that Authy is storing very little and is instead acting like a dumb "connecting layer" for installations of the Authy app to talk to each other. This is nice for security, but the consequence is that if you lose access to all your Authy installations at the same time then you're SOL.

I'm inferring this merely from using Authy for years, if someone knows more about how they work, please chime in to correct me.

We need 2FA because our password manager is not enough.

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We put 2FA keys in different password manager it works great.