Sign in with Apple isn't available on Android, so if you created your account on an iPhone using Apple — especially with Hide My Email — the Android app won't show that option.
Your account hasn't gone anywhere. For now, Report an issue and tell us:
your =username, if you remember it
the method you originally signed up with
an email address you'd like to use from now on
We can change the email address on your account so you can sign in on your new phone. Sorry for the extra step.