I think that this is an order of operation issue.
The WC woocommerce_order_status_processing fires before the WP save_post hook. ACF updates values on the save_post hook. If you try to update ACF fields on the first hook then ACF runs and updates it again and removes the value you just added.
If the ACF field is available to enter the order_shipping_number when updating the order is there a specific reason that you want to update it with code?
