External ethernet drive to plug into router for Time Machine backup

[brilliantthings]

To be clear, as far as I know the setting is not retroactive. It will affect only anything subsequently added to the library.
However there is an option called File/Consolidate that will copy referenced files into your photo library so they’re included in your iCloud Photo Library.

Select the files that you want to move into the photo library.

Choose File > Consolidate.

Click Copy.

https://help.apple.com/photos/mac/1.2/?lang=en#/pht1ed9b966d

Before you do anything else though, have you actually established whether your photos are referenced (I.e. stored elsewhere on your drive) or are managed (I.e. already included in your library)?
Either way the backup should work as advertised with the only caveat that, in the case of a referenced library, if you try to open the photo library directly from the backup drive it might not be able to find the referenced photographs as the link is broken.

Photos are not stored elsewhere on the drive. They are managed. Even with this setting, CCC backs photos up completely. With Time Machine regularly broken and Synology Drive ignoring the Photos library, I see no reason to look any further than CCC.

 

[brilliantthings]

Synology Drive backup

CCC backup