Square:
No application needed: Yes
Transparent pricing: Yes
No monthly fee: Yes
Reasonable per-transaction percentages: Yes (2.9%, 3.5% for subscriptions)
No bad reputation: Yes
Targets micro businesses: Yes
Payment button+IPN API: Yes (https://developer.squareup.com/docs/checkout-api or https://developer.squareup.com/docs/web-payments/overview)
Local payments API: No (there seems to be a REST API but not for taking payments)
Reasonably modern website: Yes
Reasonably stable business: Yes
International: Yes
No bank merchant account needed: Yes
Supports subscriptions: Yes
Supported by PHP Omnipay library: Yes
Issues: Does not allow membership of clubs which is a big deal breaker https://squareup.com/help/us/en/article/5089-prohibited-goods-and-services-with-square-point-of-sale
Notes: I think you can support Bitcoin via the user choosing a CashApp payment but it's not clear