Photos says it can't find the system library after every reboot

No Luck. One interesting thing I noticed this time -- the external Thunderbolt enclosure I have is quite loud, I never have to wonder if an external spinning drive is being accessed. When I open Photos it instantly says it can't find the system library without accessing the external drive. When I choose the option to open another library it initially only shows the default option on the system drive, then accesses the external drive and lists several libraries it's found there (mostly old iPhoto libraries plus the one actual Photos library). And again, as soon as I select the library, Photos acts like that was the system library all along. Until I reboot.

I don't have DropBox installed yet, but it doesn't use that drive.

I installed the update today, and it's out of order but first I'll mention that I set up a three photo library for a new admin account. I then moved that library to the external drive, set it as the system library, and rebooted. Photos remembered the library and that it was the system library for that account. So there's nothing fundamental about the drive that should be messing this up.

Back to my account, in 10.13.4 the behavior has slightly changed. I still get the "cannot find" message on reboot. And I think generally the first time I choose it after a reboot it's instantly recognized as the system library -- the "Use as System Photo Library" button is grayed out. What's new is that now if I close and restart Photos without rebooting, it remembers the library, but the "Use as System Photo Library" button is not grayed out, I can select this. Despite this, if I close the app it continues to sync new photos to that library in the background. Also, every time I open Photos after initially selecting the library, it opens with the "What's New/Get Started" screen as if this is the first time I've used it.

This is really seeming like some kind of permissions or corrupt settings problem in this account. Except I've done about everything I've found in suggestions along those lines.

I have used that drive successfully with Photos for maybe as long as Photos has existed. It is Mac OS Extended (Journaled) and has only one partition. It hasn't ever been a Time Machine backup drive.

If "use as System Photo Library" is grayed out, the library is already the system photo library.

Once I select it, it looks like it is. Until the the next time I reboot.

The drive is always connected and always comes up. I did have a lot of permission issues after I initially used migration agent to move my account over from the old computer, and in resolving that I tried the additional steps you mention (and a few others). That seems to have resolved the issues with about everything else (for instance iTunes and Lightroom, whose libraries are also on that external drive, work fine now).

I saw advice you'd given someone else with this problem to delete these folders:

~/Library/Containers/com.apple.Photos/

~/Library/Preferences/com.apple.Photos.plist

I tried that, restarted the computer, and followed the Apple procedure for selecting a system photo library (option when opening Photos and selecting a library). Those two folders were recreated. Unfortunately on the next reboot I once again got "Photos cannot find the System Photo Library."

Edit: for good measure I checked out the external drive with Disk Utility again, it checks out ok. And I'll reset my home directory permissions again and see if that makes a difference.

That sounded so promising! But unfortunately it didn't help. I rebooted, opened the external drive and looked at a few photos in preview, then opened Photos, and got the same "cannot find ..." message.

One additional note. After reboot, selecting the library, and closing the app:

If I option-click the app and select the library, it does not open the "get started" screen and the system library button is grayed out.

If I click on the app and open normally, I get the "get started: screen, it still remembers the library, but the system library button is not grayed out.

I'm not using encryption (FileVault is not on, System drive is formatted APFS, not APFS Encrypted). And not using screen sharing.

I'm going to reboot now and see if resetting permissions helped.

I've done the first two things you mention but not the last two, and not since the 10.13.4 update. I'll try them all just to see and what happens and report back.