As stated in the question. I know that within the GCP cloud identity API and CLI tool I can pull the list of members of a group with the following command.
gcloud identity groups memberships list --project=mygcpproject
--group-email="principal@mycompany.com" --format=csv(preferredMemberKey)
For some groups I get a return result. For others it says that group does not exist. What it really means is that I do not have rights to see inside that group. Because I know for a fact the group exists, I can see it when I run the command to show all principals within a project using:
gcloud projects get-iam-policy mygcpproject
The question is what specific IAM or groups policy do I request to have rights to see inside all the groups within my organization. All GCP examples assume that you have admin rights to everything with no real documentation anywhere that specifies least privilege required to use a specific command.
My own IAM team says we don't know what you need that's a google group thing, figure it out and ask for it and then we can research and grant. As group membership is somewhat separate from IAM principals, but a group can act as a principal I'm somewhat stuck.