The peering connection cloudsql-mysql-googleapis-com is not established when a Cloud SQL instance is configured to use Private IP

I have created a private Cloud SQL instance in an app project. The network used is a shared VPC and it is hosted in a network project.

In the shared VPC:

  • The private access connection is enabled
  • An automatic internal IP range has been allocated for private connection
  • A private connection has been created

If I go to the VPC Network > VPC Network Peering page, I don't see a peering connection named cloudsql-mysql-googleapis-com. Therefore, I cannot connect to my cloud SQL instance using its private IP address. I can only reach the cloud SQL instance using its public IP address.

The same infrastructure works for the development environment, I use terraform to generate the GCP resources. The two environments have exactly the same configuration.

Does anyone know when this problem can happen?