Photos app has stopped syncing with the cloud

Where is your Photos Library located? The default location is your Pictures. Is your Library on an external drive?

A volume is like a disk, although a disk may have more than one volume, perhaps in different formats. On your internal drive ou probably have the Volumes Macintosh HD and Data.

A Photos Library cannot be located in the iCloud Drive folder.

A Photos Library can operate from an external drive, but that volume must be formatted in either APFS format or Mac OS Extended (Journaled) format. 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.

This shows the info window ( ⌘ - i ) for my External Drive "SSK 2TB:"

and you can see that it is formatted APFS.

Let us know if any of this applies so we can see what to do next…

Bellon, Laurel wrote: … My Photos Library is located on my computer hard drive.

But where? Do you have more than one? Is this the System Library? [ It is great that you have the Library backed up! It makes troubleshooting much less risky! ]

You can get a list of Libraries that Photos knows about by closing Photos and option-clicking the Photos icon. That brings up the Library Chooser dialog:

You can see here that I have several Photos Libraries, and my "Favorites" Library is in my Pictures folder. You can also see that "Favorites" is my System Library.

If that doesn't lead anywhere, then to narrow things down, try these steps:

• 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 

Those are the easiest things to try first. Then try these:

• 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 using the Library Chooser, like above.
• Make a new user and see if the same problem recurs with it
• Rebuild your Photos Library--close Photos and re-launch by option-command-clicking the app icon.

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…

You had shown me the Info Window for the drive and I did not look, earlier. Sorry-- storage looks fine.

I would still like to know the location of your Photos Library. Where on your drive? Is it in the Pictures folder?

What results did you get when you re-started in Safe mode?

By the way-- how's the storage on your Mac? Is 10% of the storage free?

(Not connected: I had failed to notice that you are running an older OS…)