If they don't collect from buyers, they can collect from sellers. If you look back to when credit cards were new, you had them making shops agree not to charge credit card users more, despite the fees. That put cash users at a newfound disadvantage, and shops had to put up with it because card users were numerous enough.

That's exactly right. BNPLs generally charge more than credit card acquirers do, something in the 3-4% range, but the breakdown of these numbers tend to be closely guarded and that reflects outside estimates. One has to imagine Apple thinks they can command a premium here too.

With respect to cards: cards have a number of advantages for both merchants and customers. Cash is not free to handle and carries risk (theft, etc) and it's really slow. Credit card buyers tend to have larger average ticket sizes (20% larger was the last one I saw) and card buyers have more confidence buying from smaller shops knowing that they can always charge back the merchant if something goes terribly wrong. In a real way chargebacks are a big part of how we got e-commerce.

Merchant agreements generally precluded credit surcharges but they always allowed cash discounts. This is commonly seen at US gas stations to this day. They also prohibited credit card minimum purchase amounts. To my knowledge both of these are no longer true.

Shops aren't putting up with cards so much as embracing them because that's how their customers want to pay, and they don't want to miss out on a sale.