"*account* is already signed in to iCloud" in Mojave—but it's not I am trying to sign in to iCloud after having signed out. I keep getting the message that my account is already signed in to iCloud and that I should delete it from Internet Accounts and sign in again.

It's not listed in Internet Accounts.

I've signed out of iTunes

and any other app that has used this account (list these please with an edit)

I've rebooted.
Nothing seems to help so I wonder how I can troubleshoot this further.
I had the exact same issue
It only occurred on one Mac, all the others were fine.

I even removed the device from my appleid.apple.com page as well,
then it asks me to authorise the device first, before giving the exact same error.

In my case I have removed it from iTunes, FaceTime, Messages, and Game Centre.
Im not using photos or books on here.

It started after changing my appleid password. 

The fix for me was the following command in terminal:
defaults delete MobileMeAccounts

After this I was able to login again and add all my stuff back.
I have done some other steps, but as they did not help, I won't list them, unless people do have issues after this fix.
(like deleting my keychain and some terminal stuff that seems highly unlikely to help)