How to retrieve all google groups ending with @googlegroups using API

Question

I want to add members to a google group(testers@googlegroups.com) using the api. The issue is that I only need to use @googlegroups.com as the domain for google group. But seems like google only allow workspace accounts to use api. I even tried creating a workspace account and created a google group ending with @googlegroup inside the workspace account. But seems like we cant even fetch those google groups through api(I included my code below). We are only getting the google groups ending with the domain name (group@example.com). Do you anyone know or tried any workaround to add members to a google group ending with @googlegroups using api ?

Context: Google Play Closed testing needs testers to be in the google group that is added to the play console to test the app. But the issue here is that closed testing is only allowing google groups ending with @googlegroups.com. So google groups created in google workspace cannot be used to add in the closed testing.

If thats not possible can we link a workspace google group with an external google group ? so that all members of workspace google group comes under external google group ?

from google.oauth2 import service_account
from googleapiclient.discovery import build 
from googleapiclient.errors 
import HttpError
def list_google_groups(customer_id='my_customer'):
    
    CREDENTIALS_FILE = 'credentials.json'
    
    SCOPES = ['https://www.googleapis.com/auth/admin.directory.group']
    
    try:
        credentials = service_account.Credentials.from_service_account_file(
            CREDENTIALS_FILE,
            scopes=SCOPES
        )
        
        delegated_credentials = credentials.with_subject('admin@example.com')
        
        # Build the API service
        service = build('admin', 'directory_v1', credentials=delegated_credentials)
        
        groups = []
        page_token = None
        
        while True:
            try:
                # List all groups in the domain
                results = service.groups().list(
                    customer=customer_id,
                    pageToken=page_token,
                    orderBy='email'  # Sort by email address
                ).execute()
                
                current_groups = results.get('groups', [])
                
                # Process each group
                for group in current_groups:
                    group_info = {
                        'email': group['email'],
                        'name': group.get('name', 'N/A'),
                        'description': group.get('description', 'N/A'),
                        'id': group['id'],
                        'directMembersCount': group.get('directMembersCount', 'N/A'),
                        'created': group.get('createTime', 'N/A')
                    }
                    groups.append(group_info)
                    
                    # Print group details
                    print(f"\nGroup: {group_info['name']}")
                    print(f"Email: {group_info['email']}")
                    print(f"Description: {group_info['description']}")
                    print(f"Members Count: {group_info['directMembersCount']}")
                    print("-" * 50)
                
                # Check if there are more pages
                page_token = results.get('nextPageToken')
                if not page_token:
                    break
                    
            except HttpError as error:
                print(f'An error occurred: {error}')
                break
        
        return groups
        
    except Exception as e:
        print(f"An error occurred: {str(e)}")
        raise
if __name__ == "__main__":
    print("Fetching all Google Groups...")
    groups = list_google_groups()