Mac Photos iCloud sync stuck after library move

J. J. wrote: building the library from scratch using the iCloud-saved version—which seems a bit radical—I'm out of ideas.

That's a reasonable thing to do, though I've never had the need to do that. You get a nice clean Library that way, but scanning afterward takes a while.

Sometimes getting stuck is caused by a corrupted file or an unrecognized file type. This happens more with video files-- does the Library have video files in it? Older videos especially cause troubles. You could try running the videos and see if any cause trouble. Sometimes a file will look OK, but it won't go into Edit mode--that's another way to see problems.

You can make a Smart Album with

It might find something, but maybe not.

Here at some things to try to maybe narrow down the problem:

• Restart the computer (of course)
• Re-start in Safe Mode. This bypasses certain potentially disruptive processes, and it often helps. Safe Mode is different for different computers, so see this: 

           Start up your Mac in safe mode - Apple Support 

• Use another library if you have one, or make a small test Library with a few pictures in it and see if the same thing happens. You can create a new Library by closing Photos and then option-clicking on the Photos icon.
• Make a new user and see if the same problem recurs with it.  This is a bit harder, because a new user can't access a different user's stuff. You would need to temporarily move your Library out of your own user's Pictuers folder up to the general "Users" folder. 
• Rebuild your Photos Library--close Photos and re-launch by option-command-clicking the app icon. If you use iCloud Photos, it’s possible that this will cause a re-sync that lasts long enough to make you nervous.

The idea is to find out if the problem is with the Library, with your account, or with caches and login items, and stuff like that. One of these steps may fix the problem, but their failure to work also helps figure out what's happening.

Let us know what happens…

First, how is your external drive formatted? To avoid damaging the Photos Library an external drive must be formatted in either APFS format or Mac OS Extended (Journaled) format. The drive must be connected directly to the Mac by cable, not networked, clouded, NASed, etc. Additionally, the drive can not have had Time Machine on it since it was formatted. There have been so many problems with using incompatible drives that the newest macOSs won't even allow a Library on a non-Mac formatted drive to open, since there is a chance of damaging the Photos database. See this:

Move your Photos library to save space on your Mac - Apple Support

If this drive is in a an incompatible format, stop running Photos with it immediately!  A Photos Library can sit on an incompatible drive, but running it may corrupt the database.

If the drive is OK, then-- how long has it been since you moved it? When iCloud sees a new Library it has to do lots of work to make sure it's synchronized. A new OS also requires a rebuilding of the Library database and re-scanning. It could take a week or more for things to settle down.

Let us know how it's going…