When you pay by Klarna it's much the same a paying by a credit card. eBay will have been paid immediately, any arrangement to repay Klarna by instalments is between you and Klarna.
Presumably you received confirmation from eBay that your payment has been received? If so, the seller will also have been notified that you have paid.
My guess is that what your seller means is that they haven't received your payment from eBay yet. This is correct. eBay now holds sellers' payments until after items have been delivered. The quicker your seller packs and posts it, the sooner their payment will be released.
If your seller is a new seller, of hasn't sold anything for a long time, their payments may be held for longer (up to 21 day) as a security precaution, but this is nothing to do with their buyers.
Your right now is to have your item delivered. If you haven't received it by the latest estimated delivery date see below. You MUST be careful to comply with the time limits and not allow a seller to string you along with promises, because if you miss a deadline your case will be closed, and can't be reopened.
https://www.ebay.co.uk/help/buying/returns-items-not-received-refunds-buyers/returns-items-not-recei...
https://pages.ebay.co.uk/ebay-money-back-guarantee/
