Seconding andOTP[1] or Aegis,[2] if you're looking for an Android app that only handles OTP authentication. Both of these apps allow file-based import/export so that you can back up your codes and restore them elsewhere, no proprietary cloud service needed.

[1] https://github.com/andOTP/andOTP

[2] https://getaegis.app/

I'm not impressed with Authy's privacy policy, especially this part which mirrors the Google issues:[3]

> We use the information we gather from you to monitor for unusual or suspicious activity in your account, to communicate with you about your account, and as additional information that can be used to validate who you are if you need to recover your account or your account has been or may be compromised.

Authy also collects and shares more of your private information than most OTP apps:[3]

> When you use our app we collect: Your phone number, device information, and email address.

> We also share your information with our third party service providers as necessary for them to provide their services to us. We may also have to share your information with third parties if required to do so by law.

> Your information will be transferred to the U.S.

[3] https://www.twilio.com/legal/privacy/authy