iCloud storage full despite upgrade

To see how the space is being consumed, on your Mac go to System Settings > Apple Account (your account - at the top) > iCloud > Storage "Manage..." button at the top (based on OS 15.1 your view may vary). Alternatively go to iCloud.com and sign in there then scroll down to "Your Storage" for similar readout.

Then it all depends what plan you have and what's consuming the storage, for example if you turned on the option to put all your Documents/Desktop from your Mac into the cloud, or if you have a lot of photos.

How much additional storage did you purchase? Did you purchase the additional storage for your iPhone because it was reporting that it was full? If so then you need to understand that iCloud storage doesn’t increase the storage on an iPhone. An iPhone has its storage fixed at purchase and cannot be increased. iCloud is a syncing service, allowing backups of photos, music, data files, etc.