Hi
You can't open a photo library from cloud storage. Did you copy the library to the iCloud folder, or move it. (IE does the library still exist in your pictures folder?
If it does can you still open it from there?
Do you have a backup of your library (EG do you use time machine to backup your mac)?
If it is not in your pictures folder, and you don't have enough storage on your mac to put the library back, you can completely move the library to external storage with the disadvantage that you must have the external storage connected whenever you want to use photos. (in fact you should have it connected whenever you log in) You can then still use the photos app to view, manage and edit your photos.
To correctly prepare the external drive:
It must be formatted APFS or MacOS extended (journaled) (preferred for spinning drives)
It Must not be (or have been) used for time machine.
It must have the 'ignore ownership" checkbox ticked.
It should not be on a memory stick, SD or similar.
It must also not be a network drive (a direct connection is required - eg USB or Thunderbolt).
File sharing services such as iCloud Drive, Drop box, Onedrive etc are not compatible with Photos libraries.
It stands to reason that if you want any sort of reasonable performance it should be a fast drive with a fast connection.
It must also not be a network drive (a direct connection is required - eg USB or Thunderbolt). File sharing services such as iCloud Drive, Drop box, Onedrive etc are not compatible with Photos libraries.
See
https://support.apple.com/en-gb/HT201517
