Mac Photos Library on NAS

A Photos Library needs to be on a locally mounted volume. You can move the library to an external drive with a wired connection, but not onto a drive that is connected over the local network.

See: Move your Photos library to save space on your Mac - Apple Support

You can't store your library on a storage device used for Time Machine backups. And to avoid possible data loss, don't store your library on a removable storage device like an SD card or USB flash drive, or on a device shared over your network or the internet, including over a cloud-based storage service.

With the library on a remote volume you are risking data loss by transmission errors. It may look like it were working, but the library will get damaged in the background and may notice damaged items only when it is too late and the damaged files are no longer in your Time Machine backup.

As léonie says, you can't use an iCloud Library on a networked drive, because the Mac communicates with the Library continuously. But you can store a Library there if you don't tell Photos. You can run a Photos Library from a hard wired Mac formatted hard drive.

Many of us divide large libraries into multiple smaller Libraries. The smaller, more active Library, the System Library, resides on the internal drive and others are off. I keep archival Libraries on external drives which, since I use a laptop, are connected only sporadically.