The Photos Library is usually kept in the Pictures Folder.
The thing is, having a copy of the old Library on your New Mac will make Photos have to scan and compare every picture in the iCloud Library to try to avoid duplicates and conflicts. I would suggest that you create a whole new empty Library on your new Mac, and connect it to iCloud. Then this new Library will freshly fill with all the pictures in your iCloud Library, no effort involved! And you can be sure that all the files will work, since they came directly form the iCloud copy. It could take awhile.
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.

Mine has "Use as System Library" grayed out, because it already is.
Then, in Settings>iCloud, turn on iCloud and set "Download Originals," and connect it to iCloud.

I suggest "Download" originals so that you have the complete Library available for backup.
Then wait. Wait some more, and eventually this new Library will fill with full sized images from iCloud. Now you can throw away the old original Library--it's just a copy of the old Mac, anyway. And now you have a lIbrary that has all your pictures. 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 Mac plugged in and running as much as possible--overnight is good. Keep Photos in the background when you're not using it--otherwise Photos will slow downloads to keep from interrupting your work.
Tell us how it goes...