Why are my online purchases being sent to an old email not registered with Apple ID?

Safari has a cache that may have the old address. Try this path,

iPhone > Settings > scroll down > Apps > Safari > Auto Fill > edit information > Use Contact Info > enable and make sure Me contact card is accurate

Try this please, find your ME card in Apple Contacts app. Check the addresses associated with you and edit and delete as necessary.

What device did you use to make the purchase, iPhone, iPad, Mac?

OK, check these three locations please;

Each card also has an address associated with the account. Please follow this path;

iPhone > Settings > Apple ID (Your Name at top of screen) > Payment & Shipping > tap card to edit > tap Billing address > tap edit (upper right corner of screen) edit necessary changes

iPhone > Settings > Apple ID (Your Name at top of screen) > Payment & Shipping > Shipping Address (edit or delete address

iPhone > Settings > Wallet & Apple Pay > Transaction Defaults (scroll down) > Shipping Address > Edit (upper right corner of screen) > either Enter New Shipping Address, add new address or edit/delete addresses

Try these options first. Depending on device you’re using, there is one or two other possible solutions.

Did you use merchants mobile app or website? If website, what web browser did you use?