2TB iCloud storage full despite payment on iPhone 13

If you thought buying more space in iCloud would increase the available space on your iPhone, it won't. The Storage Full messages you're seeing are likely telling you you are out of space on your iPhone. It doesn't matter how much iCloud storage you buy, the memory on iPhone can never be made larger. If you are out of space on your iPhone itself, you'll have to delete things you don't need or use, such as photos, apps, mail, messages, files, music, etc.

Read this to better understand the difference between device storage and iCloud storage --> What's the difference between device storage and iCloud storage? - Apple Support (CA)

Is it iCloud storage or your iPhone storage that might be full?

What's the difference between device storage and iCloud storage? - Apple Support

If you get iCloud storage full messages, they might be phishing.

Recognize and avoid social engineering schemes including phishing messages, phony support calls, and other scams - Apple Support

If you use iCloud Photos, and have a lot of photos and videos on your phone, the “Optimize iPhone Storage” setting can help to reduce the amount of device storage your photos and videos take up.

But In general, iCloud storage is not a substitute for device storage. They have different characteristics and purposes.