making the shops pay more to use the payment service, so that the shops then increase the prices, so that you pay the same as before
Just nitpicking because I enjoy these thoughts:
When the shop increases prices, it has to do it for all the customers, including the ones without credit card. So a part of the cost is offloaded to other types of customers. While credit card customers should see a slight increase in price, it should not be as much as they saved previously. So still a net win for them, at the cost of others.
As others pointed out, the real scheme is probably entirely different.
54% of Gen Z Shoppers Use Pay Later Plans to Buy Groceries (www.pymnts.com)