For the question, I may hardly answer because I never used Google Cloud, but to me the release Repo should be configured with the config/prod_secret.exs file.
This should grant access to the database…
There should be an equivalent inside this config/prod_secret.exs of
env_variables:
DB_USER: postgres
DB_PASS: my_password
DB_NAME: my_project
DB_HOST: /cloudsql/my_project:europe-west1:my_project-sql
Then the migration is a separate task. As I mentionned in the repo I did the migration by hand using pg_dump and psql to restore database on the production server.
I have no idea about how to configure Google Cloud, but I would look if I can initialize it with a simple sql dump file.
This part, once You get it right, can be automate by edeliver.
But their are great change coming in the deployment system…