How can I share a photos library with another Apple ID?

It would be nice, but that is not how it is designed.

The only way I know of to make this work is to have the library on an external drive plugged into a single mac. Have two user accounts on the mac - one for you one for your wife, connected to your individual iCloud accounts. Both accounts should use this library as the system library.

External drive must be APFS or MacOS extended (journalled) with the ignore ownership bit set. Directly connected (no ethernet, no wifi)

See

https://support.apple.com/en-gb/HT201517

Main down side is you each have an iCloud library with all the photos duplicated - so you need double the iCloud space.

That's not currently an option. You may want to let Apple know that it is something you want by posting to https://www.apple.com/feedback/icloud.html

Unfortunately not - because you need the ignore ownership flag which (if I understand correctly) can only be on an external drive.

Without that, every time you changed user, you'd have to repair the library permissions for the next user.

You can share a Photos Library, as Tony described. It will work well for a secondary library. But you may encounter problems, when sharing the System Photos Library this way. The System Photos Library is special. Only the System Photos Library can be syncing with iCloud Photos. If you want to use the shared library with iCloud Photos, you both have to designate it as the System Photos Library.

The big problem is, that the System Photos Library will always be in use by the background processes, while you are signed into your user account. You will always have to sign out, so the library is no longer in use by you, before the other one can sign into the account; fast user switching will not be possible. And the scanning of the library for faces, objects, places will be difficult, as you cannot stay signed in while you are not using the Mac and your partner wants to use the Mac.

I would only share an archive of all photos this way, but keep separate libraries with my favourites in a smaller library, specifically selected for iCloud. My iCloud Photos Library is still small enough to fit on all my devices (but one Mac with a very small SSD), and so I can use iCloud Photos on nearly all devices without having to fall back on "Optimize Storage". My favourite photos are available on all devices, even without an internet connection.

It will, because each mac account syncs to the users iCloud which then syncs to the users phone.