When utilizing Cloud Run, what aspect is critical for establishing a private connection to Cloud SQL?

Establishing a private connection to Cloud SQL from Cloud Run requires creating a Google VPC Access connector. This connector allows your Cloud Run service to communicate securely with resources in your Virtual Private Cloud (VPC), including Cloud SQL instances. By using the VPC Access connector, your Cloud Run application can send requests to the private IP of a Cloud SQL instance rather than relying on public access. This setup enhances security by keeping the database connection internal to Google Cloud's network, protecting it from exposure to the public internet.

Other approaches, such as using a service account or implementing a firewall rule, are important aspects of managing access and security in Google Cloud but do not directly facilitate the private connectivity needed for Cloud Run to reach Cloud SQL. Similarly, deploying instances within the same subnet can be relevant for other use cases, but it doesn’t inherently create a connection between Cloud Run and Cloud SQL as effectively as the VPC Access connector. Hence, the connector is essential for enabling a secure and efficient communication pathway between these services.