Which service's primary function aligns with managing metadata for published data sources?

The answer is grounded in the understanding that managing metadata effectively is critical for the functionality of published data sources in Tableau. Data Source Properties provide essential information about a data source, including its name, description, connection information, and other critical attributes that are important for data governance and traceability.

This service ensures that users can easily understand the context of the data they are working with, enabling better data management, usability, and compliance with data management policies. The ability to access and manage this metadata allows users to make informed decisions based on the data's lineage and usage, thus enhancing the overall data experience in Tableau.

Other services mentioned, such as the Metrics Service, File Store, and Backgrounder, have different core functions that focus on metrics visualization, file storage for extracts and workbooks, and managing background tasks like data refreshes and extract generation, respectively. Their primary functions do not include managing or providing metadata for data sources, which solidifies Data Source Properties as the correct choice for this question.