[QUESTION] Is it possible to have a notify by payment?

[AndreasA]

Hi, I would like to have the option to get an asynchronous payment notification request, e.g. if the payment was successful but the user stops afterwards, e.g. Klarna Sofort has by default a "Success" message on their own page and the user might cancel after that one.
This would also mean that mails would have to be sent out then.
Also during this notification by the payment provider, the payment status has to be verified by the payment provider before it is set to paid.

I think this might be possible with the upcoming 5.x as there is a PaymentController that seems to do something like this but it doesn't yet verify the payment status.