The iCloud Library is not an off computer storage facility. It's a syncing feature so that all of your devices that are signed into the same iCloud account can have the same photos in their libraries.
If you iCloud library is complete you can restore your library as follows:
1 - create a new library on a volume that can hold the full library. (you may have to delete your old library).
2 - in the new library make it the System Photo Library.
3 - enable iCloud Library in the new library.
4 - if you want the full sized photos in the library do not enable "Optimize Mac Storage".
5 - have lots of patience while the photos and downloaded to your new library from the iCloud Library. Have Photos open and in the background during the day and leave the Mac on overnight with Photos open in in the background. Depending on the size of the library it could take a week or more to complete the download.