I'm out of the web dev game but wouldn't you just write code to search for links to the ten or so most popular wrappers for Paypal or Stripe and then an API to perform the transaction? That should cover 99% of the actual payments that happen (there are LiberaPay and crypto schemes and bank transfer and SEPA for nerds). I think that basically all the money that moves to support free webpages is through PayPal or Stripe, maybe a few percent by the EU SEPA and Canadian eTransfer systems.

Realistically you Ctrl-F "donate / Paypal / Patreon / support" and click that link. Good web design should make it clear on a screen and in the code what is site content and what is third-party content such as comments with spam links.