Well, what storage level are you paying for? Just because you are on a family plan doesn’t mean you have unlimited iCloud storage.
On your iPhone->Settings->Apple Account (your name)->check how much iCloud space you are currently using versus what your storage limit is.
And no one here is an Apple employee or Apple contractor, just fellow users like yourself. We do not have power or ability to access your account information and cannot stop e-mails you may be getting about this.
It is also quite possible, even probable, that the emails you are getting about being out of iCloud storage are scammers trying to get your credentials and data. In fact I’ve been receiving such scam emails for the last day or two. They are definitely NOT coming from Apple.