The remote server returned an error: (401) Unauthorized for Microsoft Loop SharePoint sites

The Backup of a SharePoint site displays the following error message:

Failed to initialize site processing: /contentstorage/CSP_<guid>, error: The remote server returned an error: (401) Unauthorized.

 The URL of SharePoint sites created by Microsoft Loop sites can be identified by the "contentstorage" identifier.

This error occurs when using versions of Veeam Backup for Microsoft 365 older than build 7.0.0.3007 that were not designed to handle Microsoft Loop content.

As detailed in Veeam Backup for Microsoft 365 Considerations and Limitations:

Veeam Backup for Microsoft 365 does not back up SharePoint sites created by Microsoft Loop.