Thanks for sharing your issue!
By design, Veeam attempts to restore all files that were once in a particular folder that can be restored.
Unfortunately, that’s true. Did you know that you can use File catalogue in VBR console to restore individual files instead of restoring the whole folder?
Do I need to catalog all the tapes from my weekly backups to see the data on the file server tapes?
Looks like you are right and full catalogue of tape media is required. To be honest, I’d better check with support team. I assume you should see all files on a tape, even if its being loaded to a brand new VBR server.