Hi Leo,
From the discussion it seems that after taking backup successfully backup.tly file is not getting created for you. And without backup.tly file you can't restore.
I assume you still have the access to your catalog (and all files), can you try to do a full catalog backup again and do let us know if backup.tly file is created or not.
As per your thread, you want to migrate to another mac. For this transition the only recommended way is to take backup of your catalog from this mac and then restore it to new machine. Other hacks like, copying catalog and files separately may bring some inconsistency in your catalog which might result in some bigger problems.
~Surendra