How to associate a shipping address using StoreFront CartAPI?

[ksmzn]

I am implementing a cart using the Cart API of the StoreFront API.
Even though I have sent customerAccessToken using cartBuyerIdentityUpdate Mutation, when I click on a checkoutUrl from a cart query response and go to a checkout screen, the customer's default Shipping Address is not entered.

Is there a way to associate the shipping address using the CartAPI?
Should I give up on using the CartAPI and implement the cart using only the CheckoutAPI?

Huge thank you in advance!