Add address to orders that do not require shipping

Just to round out this answer, if you change the URL to what REST requires and method to “PUT”, the REST order update is a bit easier to read.

URL:

https://YOURSTORE.myshopify.com/admin/api/2023-04/orders/{{ order.legacyResourceId }}.json

Body:

{"order":{"id":{{ order.legacyResourceId }},"shipping_address":{"address1":"123 Flow Street","city":"Shipsville"}}}