Which webhook indicates a successful Pay by Link payment?

For Pay by Link payments, just like with any other integration type, you receive the result of the payment through a webhook. An AUTHORISATION webhook event with a successful status indicates that the payment has been completed successfully.

Another way to get notified of the outcome of a Pay by Link payment is to use the email notification functionality. Please follow the steps described here: Get payment updates to your email. This will allow you to get payment status updates sent to your email, however, this is only available for Payment Links created in the Customer Area, not via API.