You can consider using the Cloud SQL for MySQL or Cloud SQL for PostgreSQL database that’s managed and scaled by Google, and also supported by Django. Both support Database Migration Service (DMS) from source databases (mysql client or psql client as test database) to Cloud SQL destination database (Cloud SQL for MySQL or PostgreSQL as production database). DMS makes it easier for you to migrate your data to Google Cloud.

You mentioned you are using the Cloud SQL Auth Proxy, which also works by having a local client running in the local environment and creates one connection to the Cloud SQL instance. The below diagram from Google Cloud shows how the Cloud SQL Auth Proxy connects to Cloud SQL:

Additionally, as per this documentation:

Django apps that run on Google Cloud are running on the same infrastructure that powers all of Google's products, which generally improves the application's ability to adapt to a variable workload.

I hope this helps.