For a developer to integrate an external application for managing store information with the B2C Commerce Staging instance, the appropriate technique is to use a POST request to the Stores Data OCAPI. This approach is used to create new store entries in the system. POST requests are standard for creating new resources in RESTful APIs, including the OCAPI used by Salesforce Commerce Cloud, which aligns with the method's definition and intended use for adding new data to a collection of resources.