Make a New System Library connected to iCloud

While iDevices can have only one Photos Library, a Mac can have many, and you can switch between them at will.  One big advantage is that you can keep Libraries of pictures that don’t get synchronized with iCloud and so don’t show up on your iPhone.

You can keep this new Library on an External Drive, if you prefer. Just make sure that the drive is 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

To make a new Library for the Mac, close Photos, option click the Photos icon, and choose Create New from the Library Chooser dialog. You can then specify an external drive as the location, if that's what you need.

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 the system library. Only the System Library can connect to iCloud.

Go to Settings>iCloud and connect this new Library to iCloud.

Set "Download Originals," to be able to get the full backup. (If you can't, and you check "Optimize," then you get only screen sized images of reduced resolution which are not good for backup.)

Then wait. Wait some more, and eventually this new Library will fill with full sized images from iCloud.

Make sure this Library has all your pictures before you trash other versions!

To open any of your Libraries in Photos, you can  use the Library Chooser, or you can just double click one.