Photos Library has moved after backing up to iCloud - can't find it

You say, "I recently set up iCloud to back up of all my documents." I'm not quite sure what you mean. Could you have dragged your Photoslibrary to iCloud? The photoslibrary can't work from a network or cloud drive. If you see photoslibrary in your iCloud folder, drag it back to the Pictures folder and, once it's re-installed, double click on it.

On the other hand, it's possible that Photos just forgot where the library is. The Library is usually in the Pictures folder, and it's probably called Photoslibrary.photoslibrary. That's the default name, but it could have been renamed. If you get to the Pictures folder and see it, just double click on it. Most people have only one Library, but if you see more than one, try them one at a time to see what you get!

If you don't find it there, try closing Photos and then Option-click on the Photos icon. You should see a dialog that lists all the libraries that Photos knows about. Again, you could try each in turn.

If you still haven't found the right library, you could do a search using Finder. Searching for photoslibrary should show all of them.

This search shows that I have five. Double click and see if you find the right one.

Let us know what happens...

Glad you found your Library! A Photos Library can'd be used from the iCloud drive or any disk that's not directly connected to the computer. So the Photos Library can't be used from network drives or cloud drives like Dropbox or Google. Photos does lots of background stuff directly with the Library, so there has to be a reliable direct connection.

iCloud Photos is not a backup-- it's a syncing service. That means that the things you do to your Photos Library on the Mac are copied on iCloud and transferred to your iPhone and iPad, etc. And vice-versa. So if you erase a picture anywhere, it gets erased everywhere-- not a backup! (Well, it really goes first the the Recently Deleted album and waits for 30 days before it gets really erased. Unless you delete it from there, too!) So if your Mac gets run over by a truck, then the pictures survive on iCloud. But if you permanently delete them from any device, there is no backup! I use a Time Machine drive that I connect to every night, and I make copies of my Libraries to another drive periodically.

To connect your rediscovered Photos Library, go to Photos Settings>General and make this Library your "System Library."

If "Use as System Photo Library" is grayed out, that's because it already is. Also make sure "Copy Items" is checked-- it should be checked by default. There can be only one System Library on a Mac, but there may be other Libraries which are not connected to iCloud.

Then in Photos>Settings>iCloud,

you should check "iCloud Photos." I have Photos on my Mac "Download Originals" so that I can back them up. If storage is a severe problem on you Mac, you can click "Optimize Mac Storage," and when space becomes limited, Photos will only keep smaller images on your hard drive, and it will download full sized images when they are needed for editing or printing. But then backups may only get the smaller images rather than the full originals.