My guess is you were accidentally using 'Klarna Financing' - that's not their main product and not what most people think of when you say 'Klarna' - it's a formal consumer-credit loan. It's like getting a car loan, rather than paying in instalments, as their main product is.
And yeah that'd be apocalyptic on your credit score - equivalent of being rejected for a car loan multiple times in a day!
It's not a big deal on credit scores at all actually. FICO-8 and the other common credit score algorithms all make the assumption that multiple credit checks in a short period of time just means the person is rate shopping, which is an extremely common thing. When I got a car last year I had ten hard lookups in a single day- this didn't do any more "damage" than a single lookup.
On top of that even hard lookups stop affecting scores pretty quickly. They really exist to prevent someone from taking out a bunch of loans without each other loan company knowing about it.
I do know that things like the Vantage score, used by credit karma and nerd wallet, put a higher weight on these checks. This is, in my opinion, purely to drive engagement to their website. FICO is what is actually used by lenders, and tends to be more stable (in my experience).
It was the 0% Klarna option (the only Klarna option) on the Google Store if that makes it any clearer. I stay away from this stuff generally so I can't tell the difference between these options when I'm trying to checkout.
And yeah that'd be apocalyptic on your credit score - equivalent of being rejected for a car loan multiple times in a day!