Photos cannot find the System Photo Library named "Photos Library"

Launch Photos with the Option key held down and in the Open Library select the library you want to open. Once opened check in its General preference pane to see if it's designated the System Photo Library.

If it is designated as such then boot into Safe Mode (How to use safe mode on your Mac - Apple Support) by booting with the Shift key held down and check there to see if the problem persists.  Reboot normally and test again.

NOTE: Safe Mode boot can take up to 10 minutes as it's doing some system cache cleaning, volume verifying and directory repairing. 

Just an add-on to OT's advice.

Did you just upgrade to Catalina? The new security measures in Catalina may be causing problems with older external volumes, if you are storing a Photos Library there.

Where are you storing your System Photo Library? Is it in your Pictures folder or are you keeping it on an external volume? If the library is on an external volume, make sure, the external volume has not been used for time Machine backups. The volume has to locally mounted, and the file system format should be MacOS Extended (Journaled) or APFS. Prepare the volume as described here: Move your Photos library to save space on your Mac - Apple Support

And you must not keep the Photos Library in any folder that is syncing with a cloud service either, iCloud Drive, the Dropbox, Google Drive.