When trying to publish an orb that relies on another private orb, the publish job (as well as the CLI) will not allow the orb to be published as it will error on not being able to locate the orb in the orb registry.
Same error as listed in a Github issue Unable to publish a Orb if it depends on an internal private orb · Issue #228 · CircleCI-Public/orb-tools-orb · GitHub
Error: Cannot find syngenta-digital/aws-ecr@1 in the orb registry. Check that the namespace, orb name and version are correct.