You don't have Cloud IAM role at the Cloud SQL instance level. You only have project level permission with access to all the Cloud SQL instance of the project. You can perform a getIamPolicy on the project to get all the policies and find which one give access to Cloud SQL
With Cloud SQL, you have users per instance, but there isn't getIamPolicy for this API
Is there a getIamPolicy for google cloud sql service? If there is how to use it?
GCP python API. Accessing getiampolicy for gcp cloud sql instance