iCloud as a Photos back-up

I just upgraded my iCloud storage to 2TB and I’m wanting to have my Photos library entirely backed up onto iCloud so that I can delete the photos from my hard drive but still access them. I also have an external hard drive that I’ve backed up everything onto, I just wanted to have the deleted pics easier to access if I wanted them. Like a secondary backup.

I can’t seem to figure out how to get my photo library to upload to iCloud so I can delete them. I’ve went into the iCloud in settings and checked off “iCloud Photo Library” and “My Photo Stream” under Photos. What am I doing wrong?