external photo library will not open

macOS 13 is even more critical with respect to the correct formatting of external drives.Older system versions may have allowed us to open a Photos Library in a location, where it might get damaged.

You may want to check, if your external drive has been correctly prepared, as described here: Move your Photos library to save space on your Mac - Apple Support

In particular:

• The file system format should be MacOS Extended (Journaled) or APFS; no other format will work. If the format is EXFat or similar, move the library to a correctly formatted volume and change the format of your external drive.
• The external drive needs a wired connection, it must not be a network share. Don't keep the library on a NAS.
• The external drive must not be a Time Machine volume, as drives used by Time Machine have a special protection and this will cause problems with the file ownershipmof the files inside the library package.