My recommendation is to stay away from the auth services that are account based such as ente or bitwarden UNLESS you have a 2nd method of authentication such as a yubikey. Why? Because you obviously can’t store, for example, your bitwarden 2FA code in your bitwarden vault. Same with ente. That’s why on android I use Authenticator Pro, as it isn’t account based and has great backup options, such as backing up to cloud and file encryption. Not sure what an equivalent would be on iOS but I’d definitely want to find out! Bonus points if it’s available on both iOS and Android.
From ente Authenticator launch blog post, they do state it is open-source.