It could also be accomplished via the Discourse API, either by adding code to handle the API requests to a server that’s controlled by the site owner, or by using a service like Zapier to handle the API requests. For example, use Paypal or Lemon Squeezy as the trigger step on Zapier, and for the action step, use the “Webhooks by Zapier” zap to send POST requests to Discourse to manage group memberships.
I’ve given answers similar to this so many times on Meta that it’s got me wondering if it might be worth creating Discourse apps for some frequently requested integrations. With some limitations, Discourse apps could function in a similar way to how Shopify apps work. The big limitation being that Shopify provides some functionality that allows apps to embed iframes on Shopify that can communicate directly with the Shopify API.
Possibly a Discourse Subscriptions app that could handle multiple payment providers would be a good proof of concept of a Discourse app.