It may take a while until the new cloud storage is available.
Wait a bit and then try again to sign into iCloud Photos as described here: Set up and use iCloud Photos - Apple Support
In addition to enough cloud storage to hold all photos from your system photos library in addition to the photos already in iCloud, you will need enough free storage on your Mac to hold all photos downloaded from iCloud.
The error NSURLErrorDomain error -999 is is typical for problems with connecting to a server. The error code -999 is given, when another process has cancelled your request. It could be a time out or incorrect or insufficient data when trying to connect to iCloud Photos.
In addition to checking for enough free storage in iCloud and your Mac you may want to check for problems with your Apple ID and problems with your system Photos Library. Is your current Photos Library enabled as the System Photos Library in Photos Preferences > general? Click "Use as System Photos Library". Is your current Photos Library in a supported location? The Pictures folder would be the best place.
