I finally ordered my iPhone 13 Pro -- but even though the Apple Store web view showed a link to my account the order was processed as a guest order.
I found there's a way to add to the order to my Apple Store account. You need to know the order number, the phone number used, and the email used.
From your account page, choose Your Orders. Since your order doesn't show, choose "Find it Now". This displays the Order Lookup Screen. Enter the order information and you will be given the option to add it to your Apple ID account.