I see you are using the Cloud SQL Proxy to connect to your PostgreSQL instance.
In the specific case of App Engine the public facing documentation offers clear instructions and code on how to achieve this.
You basically need to provide the App Engine's service account the correct permissions (the recommended role will be Cloud SQL Client) and adapt the code in your Python application to connect to the instance.
The link shared shows how to use the SQL alchemy to achieve this connection for both Public and Private IP.
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