A Klarna authorisation entails "credit risk acceptance" for a shopper, no debit of funds. Only once a capture is requested, Klarna will automatically send your shopper their Payment Instructions.
These Payment Instructions are not invoices, thus Klarna does not include the VAT amount separately.
Due to GDPR laws Klarna can not share information on the shopper's data, neither with Adyen nor with merchants. Therefore, if your shoppers need help with their Klarna Payment Instructions they can reach out to Klarna’s Customer Support. For example, they are receiving notifications, invoices, “reminder fees”...
If a shopper wants to have their Payment Instructions resent, as a Merchant you can do so from the Orders App on the Klarna Merchant Portal.