Can you programmatically add external users to Google Groups?

I am building a mailing list for customers using Google Groups. I am trying to programmatically sync customer email addresses from a contact database to a preexisting Google Group using the Cloud Identity API (link). It works for email addresses in our organization, but I am getting a 403 for non-Google addresses when invoking the create method for the groups.membership resource (link). The specific error is Error(2028): Permission denied for resource groups/******** (or it may not exist).

I am hoping that non-Google email addresses can be added to groups with the API. Below are variations of what I have tried so far.

Configuration Details

• Create a project in GCP specifically for this automation.
• Create a service account in the project.
• Enable domain wide delegation for the service account with the following scopes:
  • https://www.googleapis.com/auth/cloud-identity.groups
  • https://www.googleapis.com/auth/cloud-identity
  • https://www.googleapis.com/auth/cloud-identity.groups.readonly
  • https://www.googleapis.com/auth/cloud-platform
• Enable "Group owners can allow external members" in Groups for Business section of Admin console.
• Set "Who can join group" in group settings to "Invited users only" and "Anyone on the web can ask".
• Enable "Allow external members" in group settings.

Request Details

• Authenticate as service account (who is a group owner).
• Impersonate user from service account (user is group owner and creator).
• Set preferred_member_key.EntityKey.id to customer's email address.
• Set roles[].MembershipRole.name to MEMBER.

I have also confirmed that the email address can be added through the Groups UI. My suspicion is that it has to do with the EntitityKey (link), but I haven't found a value that works.

I could not find out whether this is possible with the Cloud Identity API. But it is possible to add external users to a Google Group using the Admin SDK, specifically the members.insert method for the Directory API (link). Just make sure that the Member in your request has type set to EXTERNAL.