@bmeddings - the Find library duplicates feature of the Find Duplicates plugin will find books in Another Library that are duplicates of book in This Library - the matching author/title criteria algorithm can be set from 'exact' to 'fuzzy'.
I use the approach I outlined to ensure the books I have just added to my Intake library are not already in the Target library before copying them to the Target library. I import a dozen or more new 'books' a day.
But based on your comment regarding TC and Calibre count differences, I suggest you run Library Maintenance->Check library on each library before doing anything else. The last phase will compare the database, which is the source of calibre's book counts (as well as its heart and soul), with the library folders and report differences. If there are any differences, you should get those resolved first.
Differences are almost invariably caused when a file manager is used to add, delete, and rename folders and files within the calibre library folder.
BR
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