How can I change my Apple ID email?

You might want to try going to your Apple ID online account,

and check that the correct eMail address is in use ok there.

Here's the link to Apple ID log-in:

https://appleid.apple.com

If needed: How to:

Get a verification code and sign in with two-factor authentication - Apple Support

If the old eMail address is still in use there too, causing the same access difficulty:

Recover your "forgotten" Apple ID online: https://iforgot.apple.com/password/verify/appleid#

More info: About your Apple ID email addresses - Apple Support

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Else:

Trouble-shooting iCloud access:

If you can't connect or sign in to iCloud - Apple Support

iCloud: About your @icloud.com, @me.com, and @mac.com email addresses - Apple Support

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If nothing above is helping:

This is an older, now "Archived: article:

What to do after you've changed your Apple ID or password – Apple Support

says: ( NB: more info under "iCloud" in the above)article)

"If you updated your Apple ID email address* before signing out of iCloud, and your device is repeatedly asking for the password to your previous Apple ID, you can temporarily change your Apple ID to sign in.

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Once you have access:

Add and manage email aliases for iCloud Mail on iCloud.com – Apple Support

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If needed:

There are "Get support" links (online chat, phone, email etc)

at the bottom of the two websites listed below:

Here's the Apple ID Support Page:

Apple ID — Official Apple Support

or

iCloud Support

All the best :-)