Photos library opening

Can you tell us a bit more background information?

Is the external drive compatible with Photos? If your library is on an external volume, the volume needs to meet all requirements described in this support document: Move your Photos library to save space on your Mac - Apple Support . Most important:

• The file system format needs to be MacOS Extended (Journaled) or APFS (for an SSD drive) - "formatted for Mac" does not suffice for libraries, only for single files.
• The external volume must not have been used for Time Machine backups or have any third-prty backup software installed
• The drive needs to have a wired connection and not been accessed over the local network. Don't even think about putting the library on a NAS.
• If you cannot enable the "Ignore ownership on this volume", your external drive is not compatible.

Are you trying to open a Photos Library or an iPhoto or Aperture Library? Starting with macOS 13 we can no longer open Aperture or iPhoto Libraries in Photos as a library, only import from the older libraries.

If you have been trying to open a Photos Library - how exactly did you try to repair the library? To repair a library on a external volume, and to be sure, that the correct library will be repaired, you have to select the library while holding down ⌥⌘ and double-click the library, not the Photos.app, to repair the selected library. Otherwise the last opened library in your Pictures folder might be repaired.

With your system photos library on an external volume you should make sure, that external drive is always connected, even after you quit Photos. The background processes will still need access to the System Photos Library. If they cannot find the Photos Library, they may create a new library in your Pictures folder.

What format is the external drive? It needs to be formatted Mac OS Extended (Journaled) or apfs, and directly connected to your Ma, not on a network share.