My iPhone storage is full

Try to free up iPhone device storage see this Apple articles below:

If you need more space for an update on your iPhone, iPad, or iPod touch

If you need more space for an update on your iPhone, iPad, or iPod touch - Apple Support

How to check the storage on your iPhone, iPad and iPod touch

How to check the storage on your iPhone, iPad and iPod touch – Apple Support (UK)

Clear Other storage on your iPhone or iPad

Clear Other storage on your iPhone or iPad - Apple Support

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

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

For iCloud additional storage, see this Apple article: Upgrade to iCloud+

Upgrade to iCloud+ - Apple Support

You cannot add storage to an iPhone. If your device storage is full, all you can do is delete stuff. Alternatively, you can purchase additional iCloud storage and upload stuff to that. You should always purchase a device with more storage than you think you'll need (assuming you can afford it).