There is no inherent limit in CC. Whether CC works acceptably with a given library size depends on the amount of memory processor memory in your device (as opposed to storage memory), the processor speed, and the complexity of the calibre metadata. I can say that at least one person has more than 30,000 books in their CC library, and several (perhaps 10-15) have more than 15,000 books.
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[Android] I have added a lot of books and now adding books takes forever. What do I do?