Veeam Backup for Microsoft 365 provides support for backing up SharePoint Online sites, but currently does not support Microsoft Loop SharePoint sites. If you are attempting to backup a Microsoft Loop SharePoint site, you may receive the “(401) Unauthorized” error.
In this case, your best course of action is to exclude the Microsoft Loop site from your backup job. You can do this by modifying your backup job settings and excluding the site in question. Veeam has provided a knowledge base article with more information on this issue, which you can find at https://www.veeam.com/kb4440.
In that KB article you will also find a hotfix available for Veeam Backup for Microsoft 365 v7 that will silently ignore and exclude these sites. Veeam is planning to add support for these Microsoft Loop SharePoint sites once the product becomes generally available.