When you try to sign in to Goodnotes using your child's Apple ID, you may encounter a block from Apple, and you might be unsure about how to proceed. In such cases, we recommend using another alternative sign-in method, either "Sign in with Google" or "Sign in with Microsoft."
Cause
If your child is under 13 years old (this age varies by region), their Apple ID can’t be used with "Sign in with Apple.” This is one of Apple’s limitations that affects all third-party apps that use “Sign in with Apple.”
If the child is part of a family group, while they can sign in to the current device with their Apple ID to enjoy shared purchases, they still can’t use “Sign in with Apple” in Goodnotes, and thus can’t get the shared Goodnotes 6 subscription/one-time payment this way, and need to use the workaround below.
Workaround
Both Google and Microsoft support child accounts for signing in to third-party apps.
Microsoft requires parents to enable the "allow sign in to third-party app" option at the child account level:
More Reference: Microsoft community
Google provides a more user-friendly experience with a prompt for permission when signing in to an app, allowing parents to approve the sign-in.
More reference: https://www.androidpolice.com/2021/06/10/google-accounts-for-kids-can-now-finally-sign-into-third-party-apps/