The permission your API key needs depends on the operation:
To list or retrieve custom metric definitions, your API key must have the View Eng Intelligence permission. Draft metrics also require the Configure Eng Intelligence custom metrics permission.
To create, update, or delete custom metric definitions, your API key must have the Configure Eng Intelligence custom metrics permission.
To retrieve, add, or delete data points, your API key must have the Manage Eng Intelligence custom metrics data via API permission.