My Apple ID email is defunct

Depending on what you did with your 'old' Apple ID.

If you have deleted it, it is no longer valid, it simply no longer exists and it no longer works.

To understand about a deleted Apple ID, see the Apple articles below:

How to delete your Apple ID account

How to delete your Apple ID account – Apple Support (UK)

See also: Understand and control the personal information that you store with Apple

Understand and control the personal information that you store with Apple - Apple Support

You can also check that 'old' Apple ID via your email box if you stil have / know, see this Apple article: If you forgot your Apple ID

If you forgot your Apple ID email address or phone number - Apple Support                  

OR see -> Having trouble signing in?

https://iforgot.apple.com/password/verify/appleid

See also -> If you can't connect or sign in to iCloud

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

If you find it, see this Apple article: Change your Apple ID

Change your Apple ID - Apple Support (SG)

Then see this Apple article: What to do after you change your Apple ID or password

What to do after you change your Apple ID or password - Apple Support

See also this Apple article: If your Apple ID is locked or disabled

If your Apple ID is locked or disabled - Apple Support (CA)

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

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

Check also ⤵️

Contact Apple for help with Apple ID account security

Contact Apple for help with Apple ID account security - Apple Support

Apple ID Support

Apple ID - Official Apple Support

If iCloud Mail isn't working

If iCloud Mail isn't working - Apple Support

BTW: Your Apple ID is the personal account you use with all Apple products and services. It includes the email address and password you use to sign in, as well as the contact, payment, and security details that you use with Apple.

You can’t merge multiple Apple ID accounts.