Which API is used to create and deploy templates or migrate workbooks from test to production data sources?

The Document API is specifically designed for interacting with Tableau's workbook files and other documents. It allows users to programmatically manipulate Tableau documents, including creating, modifying, and deploying templates. This capability is particularly valuable when migrating workbooks from test environments to production data sources, as it offers precise control over the contents and structure of the workbook.

Using the Document API, you can automate the deployment process, ensuring that the workbooks are consistent and up-to-date with the desired configurations. This API allows for actions such as replacing data sources, updating connections, and adjusting visualizations to align with the production data environment. Consequently, it facilitates efficiency and accuracy in transitioning projects to a live setting.

The other APIs mentioned serve different purposes. The REST API, for example, is used primarily for interacting with Tableau Server for tasks such as user management, permissions, and server administration. The Webhooks API is aimed at handling notifications about changes in the server state rather than directly manipulating documents. Lastly, the Analytics Extensions API allows you to integrate third-party analytics tools into Tableau, which does not focus on document management or deployment. Thus, for creating and deploying templates or migrating workbooks specifically, the Document API stands out as the appropriate choice.