PayPal Standard communicates with your WooCommerce store using IPNs ( and PDT, if you have it set up, but it’s not as common). For the most part, IPNs are still the standard method of sending information back to a WooCommerce store, such as successful charges, subscription renewals, etc.
If you want to capture and log the payload of a PayPal IPN on your WooCommerce store, you can hook into valid-paypal-standard-ipn-request like this: