Where is your Photos Library stored? " Ineligible" usually means, that the library is in a location, that is not compatible with Photos 5 on Catalina. Is your library in your Pictures folder in your Home folder, where it is stored by default?
Or did you move it to an external volume? Then the library must not be on an external volume, that is used for Time Machine backups or is having any backup software installed. The needs to be locally mounted, not accessed over the network. Even if it worked with a previous system version, it will no longer work with Catalina because of the new security features. See: Move your Photos library to save space on your Mac - Apple Support
A library may also become " Ineligible", if it has been opened by a newer version of Photos than the version that is running on your Mac. Hove you downgraded the system on your Mac or opened the library on a different mac?