How do I get rid of the fake warning messages on my iPhone 11 that keep popping up "iPhone Memory is Full" when it is not full?

Open the app switcher, find Safari and slide up to remove it.

Go to Settings > Safari > Clear History and Website Data.

Restart your iPhone.

Are you sure it says "device" storage/memory full, or, is that message referring to your iCloud storage?

See this article and check the two "storages" to understand the difference:--> What's the difference between device storage and iCloud storage? – Apple Support (UK)

Regards

Giulio

OK.... When you go to Settings > Your Name, Apple ID, iCloud, etc > iCloud > what is listed in iCloud Account Storage

When you go to Settings > General > iPhone Storage - what does it show?

Can you take a screenshot and post it?

That is a phishing pop up you picked up somewhere.