Copy photos from External Hard Drive to iCloud Photo Library

You will have two libraries, the Internal Library and the External Library on the hard drive. The only library that sycnchorizes with iCloud is the "System Library" which can be either one. The System Library is set in Photos>Settings>General:

"Use as System Library" is grayed out here because it already is.

You will have to make the External Library your System Library to copy its pictures to iCloud.

iCloud Photos is a synchronizing service. Using iCloud ensures that whatever pictures are in iCloud are also on all your devices. So if you copy those pictures to your iCloud Library, the System Library (the External Library) will have all the pictures. Your Internal Library, disconnected from iCloud, will be unchanged. But, if you ever connect the Internal Library to iCloud, then all those pictures would be copied to your Mac's Library-- you'd still have a problem with space.

So you could switch back to the Internal Library and, in Photos>Settings>iCloud choose "Optimize Storage." This will keep only smaller versions on the Internal Library, while the full sized images will live on iCloud.

But you should switch back to the External Library from time to time so that you keep full sized images on a local drive.

Let us know how it goes...