There’s normally two different fees when doing a card payment: the interchange fee (Visa, Mastercard, and the couple others), and the processing fee (Square, Stripe, PayPal, whatever).

Nowadays, interchange fees are capped to like 0.3% in the EU, but this wasn’t always the case. And for non-EU, the interchange fees are usually much higher.

So even if both a store and their payment processor is EU-based, Visa/MC is still giving at least 0.3% of your payment sum in most cases.