I tend to use $me not $self. Then the parent might become $dad or $mom.

But even better is to describe the role rather than just the position in some hierarchy. So call the App $self only inside the App package and call it $app everywhere else. Call the Widget $self only in the Widget class and call it $widget everywhere else. Call the Menu $self only in the Menu class and call it $menu everywhere else.

my( $class, $self ) in your examples looks mostly confusing to me. I'd much rather see "return $app;" so I will more quickly realize that the Menu c'tor is returning a container, not the new menu. Actually, it looks like you even managed to confuse yourself here because the Widget c'tor is supposed to return the new $widget, not the App that is stored in the (confusingly named) $self.