Transfer of Photos library to new iMac

Perfect!

Only the system library will sync with iCloud photos. I think the easiest thing to do is the following:

Since we don't know how copying over the library or the migration went (although the images may all be there the file sizes may not match exactly), it might be best to create a new library from scratch

Quit Photos

Hold down the Option Key and Open Photos (hold the key and click the icon)

You'll get a dialogue box:

Select Create New

Name the photos library something memorable (so you know which it is for later steps)

Once open

Go to Photos > Preferences > General

Click "use as system library"

Then go to id and enable iCloud photos

This will make the library you create the new default system library and then download all pictures from the cloud. Should be a win/win.

Once done, you can delete the other albums on the new Mac (those will be in your pictures folder).

Yes. Once complete you can delete the extraneous libraries on the new Mac (the ones you copied over).

If you delete the photos from the old Mac, be sure to disable iCloud photos on the old Mac first. Otherwise, they'll delete everywhere.

On the new Mac.

Open Photos

Go to the menu bar and select Photos > Preferences

Select iCloud

Is there a message there?