11 pro max saying storage is full but I have plenty of storage left.

When you say that you have plenty of storage left, are you referring to actual iPhone Storage, or are you thinking of iCloud Storage? They are two different things. What is the exact message you are seeing? If you go to Settings>General>iPhone Storage, what are you seeing?

Have you updated the iPhone to iOS 15.3? There was an issue with space calculations on the iPhone 11, and one of the later updates is supposed to have fixed that.

What happens when you tap on that notification badge? Does it take you to the first screen that you displayed? Have you attempted any troubleshooting? First step is to power the iPhone off and back on again. Second step is to force restart the iPhone. Force restart iPhone - Apple Support

I'm sorry, that is way above me. I suggest you use the Get Support link at the top of the page here to contact Apple Support, or if you have an Apple Store close by, make a Genius Bar appointment and have the device looked at.