You Added books from your old Library. As been mentioned multiple times, Calibre does not normally UPDATE the embedded metadata in the Library copy for a number of performance reasons. There are tools that WILL do that, but you need to use them on selected books.
The Question(s) Why not simply Copy the old Library folder to the new MAC?
and why did you not use the real Import/export tools built into Calibres Library Maintenance (those even do the users settings)? Or read the FAQ's before doing something major.
OK how do you recover? depends on what you have.
If you have the OLD library FOLDER (includes
metadata.db)
Simply copy it to a brand new folder (path).
DO NOT just drop the files into an existing Library,
then switch/Create: Use existing <path>.
If there are no New books (or are willing to lose any changes) you are done
If you need help Merging additions, come back and explain what you need. (updating metadata of those preexisting is not easy)