The error message “Cannot change WebPart ExportMode to ‘All’. WebPart will be skipped” indicates that a WebPart cannot be backed up due to an issue with custom scripting when using Veeam backup for Microsoft 365.
To resolve this issue, you must enable the “Allow custom script” option in SharePoint, as detailed in KB article from Veeam: https://www.veeam.com/kb4091. Once enabled, you should be able to successfully back up the affected SharePoint sites.
Alternatively, if you do not need to backup custom Web Parts content, edit the Organization and uncheck the option for Allow this application to enable export mode for SharePoint Web Parts.