You are not using Gmail API. Gmail API is intended to interface with a Google user's Gmail mailbox (sent/received emails). OAUth scope email does not grant you any access to Gmail API. What it does allow is access to get the Google user's email address (may be @gmail.com or may be another domain).
See Google's list of OAuth scopes. email is listed under Google Sign-in.
To my knowledge, there are no quotas around usage of email scope and sign-in.