Re: "The default email for receipts and communication is an old email address.
Where else can I check to remove this old email and use the primary email/Apple ID?"
You may want to try logging-in to your Apple Account online, and check / edit / your details listed there:
Eg: See if the old eMail address is still listed in your contact details
or
Look for the Billing Address in: Payment and Shipping > use "Edit" to make any changes
https://account.apple.com/
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If you still need help:
Wondering if you purchase items from the Online Apple Store, or physically visit an Apple Store nearby ...
Apart from your Apple (ID) Account:
Seems possible you may have a separate hardware-purchases account ?:
For online purchases: See Apple Support's article: Your Account - Shopping Help - Apple
For local in-store purchases you may need to phone the store listed on receipts, (or in emails?)
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If all else fails: You could try reaching out to the Billing and Subscriptions Support team:
There's a "Get Support - start now" link (online cat / phone / email etc. ) at the bottom of their website:
Subscriptions and Billing - Official Apple Support