Explanation
Adding a new user to the engineering organization in DTR will not automatically grant them read/write access to the engineering/api repository. This is because the repository permissions are not inherited from the organization level, but are configured separately for each repository. Therefore, to grant read/write access to the new user, you need to add them directly to the list of users with read/write access under the repository's Permissions tab. References:
* Docker Trusted Registry - Manage access to repositories
* Docker Certified Associate (DCA) Study Guide - Domain 3: Image Creation, Management, and Registry
https://docs.docker.com/ee/dtr/user/manage-repos/#manage-access-to-repositories
https://success.docker.com/certification/study-guides/dca-study-guide#domain-3-image-creation-management-an