Which method should be used to call the Cloud Storage API from a Compute Engine instance without a public IP address?

To call the Cloud Storage API from a Compute Engine instance without a public IP address, Private Google Access is the appropriate choice because it allows you to access Google services like Cloud Storage directly over the internal network. When an instance is part of a VPC network and has Private Google Access enabled, it can send requests to Google APIs using the private Google services IP addresses instead of requiring a public IP.

Using Private Google Access eliminates the need for a public Internet connection, which means your Compute Engine instance can remain secure without exposing it publicly while still being able to utilize essential Google services. Private Google Access is specifically designed for scenarios where you have internal resources that need to access Google services without the need for public IP addresses.

Carrier Peering and VPC Network Peering are more focused on connecting networks or services and do not directly solve the problem of accessing Google services privately from an instance without public IPs. Shared VPC networks are used to allow resource sharing in a Google Cloud Organization and do not specifically enable private access to Google APIs for instances without public IPs.