It may happens that your order won't be updated directly on your marketplace, the reason for this is actually super simple! 🙌
In case the hourglass over the marketplace keeps remaining, verify the following steps:
Access to the left panel of WooCommerce Dashboard and click on WooCommerce > Settings.
Click on API tab.
Click on Keys/Apps and then click on the existing API Key.
Set the permissions to "Read/Write" and save.
Then try to update the orders again from Shipping Labels section clicking on Action > Update Marketplaces with shipments info: