Apple TV (sometimes other Apple devices): Keeps asking for my old iCloud login details
I decided to migrate to a new iCloud account a while back (didn't like the email I chose) but when I setup a new Apple device or use my Apple TV I sometimes (actually it's often for the Apple TV) get a login prompt asking to sign into that old AppleID I don't use anymore. It's frustrating as I have to click a few times to dismiss it as it badgers me to sign in. Same issue when I setup a new iPhone it asks me to sign into that account too.
Does anyone have any idea of how I can stop this behaviour and remove it from any other device setups in the future? I tried searching on here but maybe I haven't searched with the right term.
Apple TV HD, tvOS 15