Ensure that the service account you are executing Terraform with has the "manager" role for the Group.
You need to do this via Cloud Identity (Workspace) Admin Console and not via the Google Cloud Console IAM.
Alternatively use: POST https://cloudidentity.googleapis.com/v1/{parent=groups/*}/memberships
as described in the Cloud Identity API documentation
Once the user has the access you can add run the group via: terraform apply -var=customer_id='ID_FROM_IDENTITY' -var=group_name='[email protected]' -var=project=project-01-1
The customer_id
can be found https://admin.google.com/ -> Account -> Account Settings
This Terraform will add a service account and add it to the existing group.