OK, I've found this page with some explanation, why my new Requests are not visible in Portal (and Customers don't get any notifications even if they are Reporters) - they don't have Request type for this Issue type.
HOWEVER, what I don't understand - why my previous identical requests (without Request type as well) WERE visible in the Portal and notifications were sent to the Customers.
See a previous "bug" Issue type and nothing as Request type assigned (same people participating) - viewable in Portal:

And the new "bug" with same story no longer visible in Portal (notifications not working either):
