iCloud storage full despite family plan?

The Family plan is not unlimited. It can still get full if you are storing a lot of stuff on it.

If you go to Settings ➜ Account ➜ iCloud ➜ Manage Storage what does it say you have used?

Are you sure it's complaining about iCloud? Maybe it is saying your local iPhone storage is full?

click here ➜ Manage your iCloud storage on your Apple device - Apple Support

Please do not post your email address in a public forum unless you want tons of spam and scam emails.

This is a user to user forum, you are not addressing Apple Support. We cannot delete anything for you.

If you changed your Apple Account, make sure the new one is logged in to the devices correctly in Settings ➜ Account.

If your subscription is tied to a different account, or is accessing the storage through family sharing, make sure the iCloud account and the ac count for Media & Purchases are the same.

Apple has a way to change the email address on an old account but it appears that you did not do that and instead created a new account. The support article Change your Apple Account primary email address - Apple Support outlines various methods for changing the email address (Apple ID) you use for your Apple Account while retaining everything in your account.

The best thing to do is go back to using the old account and delete the new one (How to delete your Apple Account - Apple Support. However, since you cannot easily re-use an email address that has been used for a deleted account, you will need to get yet another email account to use as a new address with the old account.

As for the iCloud full message, depending upon which plan level you have and how much storage you are using, having a second account effectively doubling your requirements may have resulted in you exceeding the plan limit.