It just takes a very, very long time for photos to analyse each and every image to find out, what kind of scene it is and recognize the objects and the the people in the photos. The more photos you are having in your library, the longer it will take. Just let Photos run at all times, so it will eventually finish. Even, it
If it will eventually finish, it will start again, when you add adjustments to your photos or import new photos. For my largest library it took several month, for a small test library with just 1000 photos it finished in two days.
It does not matter, you can work with Photos, before the scanning of the library has finished.
I would just make sure, that your library does no longer contain videos or older photos, that Photos 5.0 on Catalina cannot handle. All legacy media files, that are incompatible with macOS 10.15 Catalina should have been removed and converted to a more compatible format, before you upgraded to Catalina. Lookout for items with white thumbnails or an album or folder named "Unable to Upload". This will show you items that cannot reprocessed and might block the scanning of the images and videos.