Photo system library on a NAS

Photos Library has not been designed to support network access. Also TimeMachine-formatted volumes, and non-Mac formats like exFAT and NTFS are not supported and might corrupt the library.

APFS and MacOS Extended (both case insensitive) are supported -- also make sure the external volume's Finder > Get Info is "Ignore ownership on this volume".

Photo Library vs NAS - Apple Community

Is it possible to add a network folder to… - Apple Community

svdlfilm wrote:

Can I move my Photo Library from my MBP to said NAS?

Yes. Ref: Move your Photos library to save space on your Mac

And can my partner access that NAS and the shared library too from her iMac?

Potentially, yes.