How do I change the default shipping address on my account?

The "Apple Card" just like any other credit card only has the address they send bills to. The only thing that credit cards send you are new credit cards and bills, with the Apple Card it's just the New Card. An "Apple ID" has a shipping address only as far as "Apple Store" purchases. Any time you make a purchase from anywhere including the Apple Store you can select a shipping address. If you use "Apple Pay" that default shipping address is in the Settings for "Wallet & Apple Pay". But again, for each purchase that can be changed as well.

Okay, Apple Card, not Apple ID.

AFAIK, there isn’t a (different) shipping address, but use the message function within the Wallet app and ask the Apple Card folks directly.

Manage your Apple Card account - Apple Support

Confirm the address on the payment account. Apple tends to ship only to the address associated with the payment.

There are several places to choose it. For instance, for Apple Pay, on your iPhone go to Settings - Wallet & Apple Pay > then scroll down to shipping address. The shipping address is completely separate from the billing address. My shipping and billing address have been different since 12/31/2019 with no problems at all. For the Apple Watch goto the "Watch" App then scroll down to "Wallet & Apple Pay" then in there, just like the iPhone scroll down to shipping address. On the Mac it is similar go to System preferences - Wallet & Apple Pay, click on Contact and Shipping on the left lower panel. The Actual Apple store can be different, unless you always use Apple Pay for the Apple Store, then your shipping address will flow from apple pay. I was told by support that if you change the "default" shipping address for one device they all should change as long as they all use the same apple ID.

Also, for just one purchase such as a gift, you can change the shipping address for just one order while you are paying with apple pay. Practice without confirming an Apple Pay Purchase. Practice with something cheap that you might need.

In addition, your "Apple Card" only has a billing address. "Apple Pay" is where the shipping address comes from. I'm sure this is what you are looking for.

Note: I edited the location on the Apple Pay Screen on the Mac, I said right, when it was left.

Note: I have many issues with the "Apple Card", fixable issues, like changing a payment to the day before. Currently this can only be done over the phone with Goldman Sachs. But, I have no issues with "Apple Pay", that is where any shipping address would be identified, and that Shipping address is for all your Apple Pay Cards. not just the "Apple Card".