Storage full notifications despite paid storage on iPhone

1. Paying for iCloud storage does not mean it cannot be filled up too.
2. Paying for iCloud Storage has no bearing or effect on your iPhone's local storage capacity. iCloud Storage is in the cloud, on an Apple server somewhere not on your iPhone.

• • click here ➜ What's the difference between device storage and iCloud storage? - Apple Suppor

3. Software updates need storage locally on your iPhone, they do not use iCloud storage.

4. If your iPhone is low ion storage, the you need to delete content from it or move it out to an external drive or computer, not buy iCloud storage. That's like renting a warehouse to keep stuff in and an expecting your house to now have an extra room for you to store it.

• • click here ➜ How to check the storage on your iPhone and iPad - Apple Support

You have two levels of storage - there's the storage built-in to your iPad, and there's iCloud storage which is used for backups, content sharing, and offloading little-used data.

You can pay all you want for iCloud storage, but it won't make any difference to the internal storage on your device, and it sounds like that's what you're getting notifications about.

What you need to do is offload some idle content from your iPad.

iOS will do some of this for you. Check Settings -> General -> Storage and configure things like offloading photos and unused apps to clear idle space.