I am currently unable to sync photos from my Mac (running Catalina) to my iPhone (13.1.2).
There is no issue in downloading photos from the iPhone to the computer. My Photos Library is actually located on an external hard drive given space issues. Synchronization had been working and suddenly stopped (slightly before the iOS 13 update – and well before I upgraded to Catalina).
I do not use iCloud for photos. I have set the Photos synchronization from the Finder menu for photos to "Sync photos to your device from: Photo Archive" where photo archive is the name of the external drive where the photo library is located. I have selected to "Sync All Folders". Nothing happens when I click "Sync". There is a quick spinning wheel to show progress and then it stops.
Oddly, the iPhone is reporting about 9 gigs of photos, but nothing is available on the phone in the photo app. There should be about 35 gigs of photos (35,000 in total)