Apple ID and synching across devices

I hope someone can help because I am going crazy trying to figure this out.

Three days ago I was locked out of my account whilst trying to update the email I use for for my Apple ID: this was on my MacBook. This morning I received a text and email saying I could now update the password, which I did but it has only worked on my MacBook.

My phone (XR), iPad (Air 3) and watch (series 4) all point to the old email address. I cannot log out of these devices in order to log back in with the new ID, because they are all using the old email address ID. I fear if I click "I can't remember my password" (I can remember it), it will trigger me becoming locked out again.

It seems that I'm in some terrible limbo between ID with the old email and ID with the new email but I don't know how to fix it. Incidentally, my phone doesn't appear in the list of my devices when I log into iCloud (with new email) through a browser.

Can anyone help me please?