Photos App (or OS X) does not unlock library

For starters the Photos library can not be access wirelessly - it must be on a local drive connected with a fast wired connection or internal - Where is it safe to store a Photos Library? Requirements for the external drive

And Photos is not a multie user program and does not work well with different users accessing a single library

The "library 1" in our example stays locked until the user who worked with it is logging out completely.

Correct - until you log out there are possibly (probably) Photos background processing going on requiring access to the library

The only supported way to share a library is using iCloud Photo Library with all sharing users logged in with the Same Apple ID

LN

Quitting Photos and closing the library does to suffice to release the library. Your system Photos Library will be in use as long as you are signed into your Mac. You have to log off to release the library. The drive with the shared library should have the "Ignore ownership on this volume" flag set, as described here.

Sharing photo libraries among multiple users - Apple Support

Apple advises against storing the Photos Library on a network share, just like previously for iPhoto Libraries and Aperture Libraries.

This is also documented in: Sharing photo libraries among multiple users - Apple Support

Connect an external USB, FireWire, or Thunderbolt drive which has enough free space to contain the library.
Be sure to choose a locally mounted drive. Storing your library on a network share can lead to poor performance, data corruption, or data loss.

If any user opens one of the libraries, let's call it "library 1", on the shared drive or local on the MacMini,

To share a library at all, it needs to be on locally mounted drive or in a separate partition of the system drive, with the "Ignore ownership on this volume" flag set. Is that what you are doing?

See: https://support.apple.com/en-us/HT201517

And log off, when you finish to work with Photos, to terminate all Photos processes. Quitting Photos is not enough.

I'm actually not sure whether it's background processes locking the library, because the user who opened an locked a library can open other ones and the background processes would focus on the last library opened, wouldn't they? Well, unless there's a bug, blocking that...?

As far as I can tell, the background processes are primarily working for the system library (the Photos library used with the Media Browser or iCloud services). Then the library will be in use, as long as you are logged in. if you are not using iCloud services with your Photos Library, consider to make a different library the System Photos Library. This will stop the icloud processes from blocking your library.

Quitting an application does not ensure that it really terminates. This has been the way since MacOS 1O.7 Lion. Quitting an application will just tell Mac OS X that you no longer need the application running, but MacOS X may keep it cached and ready to resume, nevertheless. Only logging of will terminate the applications for sure.

This new process model of "Sudden Termination" and "Resume" has been introduced with MacOS Lion, It is quicker to go straight for a restart of the system, to be sure, that not a cached version of an application will be resumed.

( http://arstechnica.com/apple/2011/07/mac-os-x-10-7/8/#process-model)

Ownership is turned of on the USB-connected drive.

But in your original post you said "or shared via network". Are you using the drive alternately over network or USB? Network access is simply not supported.

the support page is for multiple users on one computer, not for multiple computers, and only for direct wired connections, not for network as you have

We have two Macs, a Mini and a Macbook, which we use in our family. The Mini has an external Raid Drive. The content of the drive is shared in our home network, including several Photos libraries. The main users, my wife and myself to have admin rights on the machines.

and it is an old article that predates High Sierra which uses more back ground processing that previous versions did

again you are trying to do something the Photos is not designed to do

And Photos is not a multie user program and does not work well with different users accessing a single library

Simply, the photos library is not designed for network access. End of story. That it worked for you in the past was pure luck.

and as to this strange post

Accessing a library on a network drive improved a lot since the first version of Apple's Photos app. Even though I'm no developer it works good enough for us.

I believe the reason you posted is that it is not working for you - and the reason is that you are doing things that are not supported and do not work

LN

My question/issue is what is keeping the library locked? It worked without logging off in the past?!?

I have always had to log off to be able to access my photos libraries from my second user account, at least for the system photos library. It has been this way for me, ever since I switched to Photos. perhaps we are using Photos differently. And the background processing may settle down after a few weeks. Directly after the upgrade the photosanalysisd will be running a lot, scanning for categories and faces, also the video conversion will rerunning, if you are using the new codecs HEIC or HEVC on a synced IOS device.

Simply, the photos library is not designed for network access. End of story. That it worked for you in the past was pure luck.