Not sure where that pricing comes from. I believe Square's payments API is priced the same as Stripe (I'm sure that's not an accident):
https://squareup.com/us/en/townsquare/payment-api
> Square’s payment APIs are free to integrate into your software. For online sales, the only cost is 2.9% + 30¢ per payment transaction. Sales made with Square’s POS app are charged at our standard fees: 2.6% + 10¢ per swipe, chip card dip, or NFC payment. Manually entered transactions are charged at 3.5% + 15¢.