DBMS_RESOURCE_MANAGER_PRIVS is the specific package used to grant resource group privileges and administer the Resource Manager. It provides procedures like GRANT_SYSTEM_PRIVILEGE and GRANT_SWITCH_CONSUMER_GROUP to authorize users for resource management tasks. The other packages listed serve different purposes - DBMS_REPCAT packages handle replication, while DBMS_RESOURCE_MANAGER creates and configures plans but doesn't handle privilege grants.