Klarna Payments accepts orders only for customers with billing addresses in the markets that match the currency of the order, per docs.
Klarna Payments integration is an alternative payment provider in Shopify, and Shopify limits Klarna Payments, as for all alternative payments methods, to always using only the store’s base currency, per: Shopify multi-currency docs.
As such, if the store base currency is SEK, Klarna Payments will be able to accept orders for customers whose billing country is Sweden. Customers with addresses in other countries will receive an error message, e.g. as shown in the screenshot below. The exact error message may be dependent upon region & Klarna product, i.e. such as “Option not available” or “You need a US billing address to use Klarna”.
After Shopify redirects to an alternative payment integration, such as Klarna Payments, when a customer places an order, stock inventory can no longer be guaranteed as the inventory is not locked in the Shopify store. With the upcoming new payments integration, payments apps cannot query the Shopify store's stock inventory via API. In the future, Shopify will be updating checkout to avoid oversells for alterative payment methods.