I believe you that Klarna are shady about how they manage data, however, my understanding was that they got a banking license because they want to fund themselves via brokered deposits? A banking license means that they can get money from anyone in the EU and it will be insured up to €100,000. Without this, almost no one would want to deposit with them.

If you have other information about other reasons they might have become a bank, I would be genuinely interested in hearing them.