The connection manager causes problems if the user is not registered and goes directly through the connection. (in my case it is with google auth).

It does not ask the user for the minimum age to register.

This is annoying because under the GDPR we must not process the personal data of children under 16 years old.

Is there anyone else facing this problem?

The only option for that would be not to use google login. Generally with external registration methods, they will not allow any extra checks other than their own