Do you have plenty of free storage? Photos will need some additional storage while upgrading the library.
Is your Photos Library an iCloud Photos Library or stored locally?
Sometimes it helps to repair the permissions of the Photos Library manually from the "File > Get Info" panel, before you can upgrade the library.
- If you select the library in the Finder, ctrl-click it, select "Show Package Contents", you can set the permissions for all items in the window with the library contents individually to read & write for you.
- For the folders in the package use the option "Apply to enclosed items".
Change only the permissions and nothing else.
A common problem with Photos after the upgrade to Catalina are incompatible media files in the library. Photos cannot handle any longer some video formats and image formats, that have been compatible with Photos 4 on Mojave. Did you check your library for image files and videos, that are incompatible with Catalina?