Note that I’ve used the API to fill up the phone number on the customer, I also have the phone number on the shipping address. But still the contact information field on the admin page empty. Any ideas?
The contact information on an order are populated by the phone and email fields on the Order object. This is separate from the phone number in the shipping address or the phone number attached to the customer. You can read more about these fields here: https://shopify.dev/api/admin-rest/2021-07/resources/order. Hope this helps!