The Password* Manager feature that I use in the iPhone default application is not for storing seed phrases but for storing usernames/emails and passwords for access to certain accounts so that they can be automatically filled in when I want to log in. To open the Password feature, I set it using Face ID. Of course, I use other applications for accounts that use additional 2FA, and so far, I have used Authy.
I believe this uses an Apple account just like MacOS right? I also use them on my Macbook but I don't trust them enough to move all of my passwords over, not to mention I use other devices other than iOS/MacOS too. I also use Authy but I'm in the process of moving my OTP to FreeOTP and Aegis Authenticator. It takes a bit of time since they don't offer an export or backup feature at all.
For 2nd factor authentication, I abandoned Google Auth and started using
Strongbox to store my passwords and 2FA codes. It's easy to set up and has the option to export the code from backups via a link.
Meanwhile, with Google Auth, you're stuck with them only. You can only sync the same codes saved on another device with your account.
If you don't want to change the 2FA code for your accounts, but want to export it to another app, like iOS Passwords, you have to select the account you want one by one or all at once. Auth shares the link via QR code and no text option. You have to find a way to get the code via QR code with another device like a laptop or cell phone to get the code in text... it's a lot of bureaucracy, the worst authenticator I've ever used!