Can you please let me know what type of file-system format you are using on all of your drives? For the iMac and the Mac Mini, are the drives formatted as Mac OSX Extended (Journaled) or something else?
What format are you using on the external Seagate HD?
I would try to authorize the previous iMac and perform a manual backup as @mjw suggests. Please let me know if this works.
I wanted to check in here with you and see if you were able to create a fresh backup by re-authorizing your iMac. If you have not yet had a chance to do so or if something went wrong with creating a fresh backup, I may have an alternate solution as proposed by our QA team.
Can you please post a screenshot of the backup directory listing? This listing should look something like this:
Inside this listing there should be a _roon_backup_ file towards the end of the list, can you please let me know if this file is there in your backup and post a screnshot? If you can confirm that this file is missing, I can send you a replacement for that file since it is a standard file across all backups.