The new Klarna payments app integration for Shopify provides integrated order management. Order management for Klarna orders should continue to be processed as part of your standard order management within your Shopify admin. Orders marked as "Paid" or "Authorized" are guaranteed funds by Klarna and can be fulfilled when appropriate for the shop; orders marked as "Payment pending" should not be fulfilled yet, as payment has not been completed and is not guaranteed by Klarna.
(While order management could be done directly via the Klarna merchant portal, this will cause Klarna data and Shopify order data to be out of sync and could result in unintended updates, e.g. duplicated refunds. Unless there is a problem, all order management should be done through the Shopify admin, not the Klarna merchant portal.)
Based on the "Payment capture" method configuration setting (in the Shopify store admin, under Settings -> Payments),
This "Payment capture" setting applies to ALL orders in a Shopify store.
With this new payments integration, the capture of the Klarna order is no longer based upon the Shopify order being fulfilled / shipped (as was previously dependent with the HPSDK integration). If you'd like have the Klarna order based on Shopify order fulfillment, you may be able to build that specific to your store using Shopify Flow. If you utilize a Shopify Flow to capture the orders, please be sure to note the recommendation here.
Note: based on your Klarna contract, Klarna charges merchant fees for captured orders. When Shopify orders are automatically captured (immediately after the order is placed), Klarna fees will apply for each order, even if the order is cancelled in the Shopify admin without being fulfilled.
If using the Shopify Flow app to trigger the capture of Shopify order (when "payment capture" method is set to "manually"), a time delay (~30 minutes) should be included after the "Check if" payment method is "Klarna" step, to avoid the Payment gateway sometimes set to null in some Shopify webhooks, e.g. for webhooks used by apps like Signifyd.
Refunds made in Shopify (all types of Shopify refunds: before or after Shopify order fulfillment, full or partial refunds, order line based refunds or amount based refunds) will update the Klarna order after a short time delay of a few minutes (less than 10 minutes).
The Klarna refund does not include order line data (as refund order line data is not shared by Shopify).
For orders that are not automatically captured (based on your store's Payment capture setting), Klarna recommends manually capturing the order prior to the Klarna order expiration date (that expiration time frame depends on your Klarna contract, e.g. 28 days). The Klarna order's authorization time cannot be extended within the Shopify admin; Klarna orders may possibly be extended in the Klarna Merchant Portal, if applicable for the order.