You must have a Global Admin (GA) on the M365 Tenant with an Exchange License for the “Add Backup” page to list the Public Folders.
We can’t access Public Folders through Exchange Web Services (EWS), which is why a Global Admin is required to Backup Public Folders. Public Folders are backed up through Exchange Web Services (EWS), and those Public Folders with criteria “FolderClass = IPF.note” are located under the Root Folder alone and can be backed up.