According to the documentation:
"Cloud SQL automatically ensures your databases are reliable, secure, and scalable so that your business continues to run without disruption. Cloud SQL automates all your backups, replication, encryption patches, and capacity increases—while ensuring greater than 99.95% availability, anywhere in the world."
This means the underlying Operating System will receive patches and security updates, will be scaled as required, the ability to restore your instance etc.
What you run inside the database will be the responsibility of the user. However, GCP provides tools that a user can leverage to optimise queries such as slow query flags or general database configuration.