Something you might not expect is that, unlike on a phone, there can be several Photos Libraries on a Mac. But the only one that can connect to iCloud is the "System Library," and that's the Library that's available to other apps for uploading images and such. The Libraries are located in the Pictures folder on your Mac-- you may see that there are some Libraries that were made by accident.
So, your best bet is to create a brand new, empty Library, designate it as your System Library, connect it to iCloud, and then sit back and let it fill up with your pictures from iCloud. Here's what you do:
To make a new Library for the Mac, close Photos, option click the Photos icon, and choose Create New from the Library dialog.
A new, empty Library will open. Then, on the Mac in Photos>Settings>General, you must make this new, empty Library your System Library.
In this picture "Use as your System Library" is grayed out, because it already is my system library. Only the System Library can connect to iCloud.
Then on the Mac in Photos>Settings>iCloud you need to turn on iCloud and to set "Download Originals,"
(If space on your Mac's drive is a problem, you can choose "Optimize Mac Storage" in the iCloud menu. This will keep only smaller images on your Mac, so your pictures will be harder to back up.)
Then wait. Wait some more, and eventually this new Library will fill with full sized images from iCloud. All your pictures from iCloud will be there! Depending on the size of your Library, you may have to wait a week or more, but the Library should tell you when it's finished syncing. It might say something like this
at the bottom of the Library view. Leave the MacBook plugged in and running as much as possible--overnight is good. Keep Photos in the background when you're not using it--Photos will slow downloads to keep from interrupting your work.
If you have other Photos Libraries on your Computer, then you may want to double click on each one and see if it's something you want to keep. You can trash the Libraries, or keep them if you like.
