Apple absolutely does not provide Apple Card in-house, and in particular is not loaning you the money when you use it. Among many other reasons, for that to be legal would require Apple to be a bank, which they're not and they definitely don't want to be, because being a bank is a huge pain, and in particular means signing up for an extremely heavyweight regulatory compliance regime.

Apple Card is the result of a co-branding deal between Apple and Goldman Sachs (which is currently in the process of exiting the deal and being replaced in that capacity by JPMorgan Chase). Apple provides the branding and some minor fintech features; Goldman (or in the future Chase) issues the card and is on the hook if people don't pay their credit card bill.

Presumably for this particular program using Klarna was cheaper because Klarna already specializes in precisely this kind of transaction.