First the "jokes"

 //Works!
 ...
 //Does't work!
 ...
[download]

Now back to the question :)

...
my $ext = SUi::Ext->new();
[download]

Why are you creating another controller instance inside a controller? Why aren't you passing any arguments to the constructor?

https://metacpan.org/pod/Mojolicious::Controller#ATTRIBUTES

Lets see what the source tells us

$ perldoc -l Mojolicious
...\site\lib\Mojolicious.pm

$ ack "con\S+\bnew" -in ...\site\lib\mojo*
...
...\site\lib\Mojolicious.pm
73:    = $self->controller_class->new(app => $self, stash => $stash, t
+x => $tx);
531:  my $c = $app->build_controller(Mojo::Transaction::HTTP->new);
532:  my $c = $app->build_controller(Mojolicious::Controller->new);
560:  $app->dispatch(Mojolicious::Controller->new);
569:  $app->handler(Mojolicious::Controller->new);
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Hmm $self->controller_class->new(app => $self, stash => $stash, tx => $tx);

Maybe you simply want to subclass SUi::Ext, to make SUi::Ui a subclass of SUi::Ext, as in use Mojo::Base 'SUi::Ext';