For Ansible Controller, the endpoint is /v2/role_team_assignments/ but I cannot see permissions that I've assigned that relate to EDA.
I have checked gateway API endpoints; it seems that there is no way to retrieve the built-in role list to get object_id.
It probably needs a new API to get the built-in-role object_id to assign it to the team via API.

FYI...Checked it with a test lab but could not find Role Team Assignments for EDA with Web UI. Also, I was able to find the API Endpoint for Role Team Assignments for gateway from the link below.
https://<Controller_URL>/api/gateway/v1/docs/#/role_team_assignments
But could not find the API Endpoint for Role Team Assignments for EDA.