Which event should we subscribe to if we want code to be triggered when a new user registers?
AccountEvents::SET_USER isn't the event for user registration. Per the docs:


  This event allows modules to perform an action whenever the current user is
  set. The event listener receives an \Drupal\Core\Session\AccountSetEvent
  instance.


The event is fired when Drupal initializes the user object for the current request, not when new users are created. 

For responding to new user creation, you can still use hook_user_insert().