iCloud will automatically back up the files you save in the Document directory. You can try to put the CoreData files in this directory.
However, due to the recent review, if the cache file is too large, it will be rejected.
This week, it was rejected due to this problem. The two solutions are to set up not to back up but not use your scenario
It is said that you can appeal to Apple and say that I really need to synchronize this information in iCloud, but it depends on the mood of the reviewer