Today Apple released iOS 16, iPadOS 16 systems, and has released the first developer preview Beta. In iOS 16, Apple gave users the option to use third-party authentication apps with built-in passcode functionality in the Settings app.
This allows those who prefer authentication apps like Google Authenticator or Authy, or Microsoft Authenticator to set it as the default and get codes from those apps when using the two-factor authentication option with a password.
The third-party authenticator app option is available as an alternative to the built-in iCloud password and keychain functionality and can be used as the default when setting up verification codes.
iOS 16 and iPadOS 16 are scheduled to release public betas in July, and developer preview betas are currently available. iOS 16, iPadOS 16, macOS Ventura, and watchOS 9 will all be publicly released this fall.