I expected that the call to new would wind-up executing the code in Foo which would, by means of $class->SUPER::, invoke the one in Bar...

But it does. What makes you think it doesn't? I cannot deduce the problem from your code snippet.

use 5.010;
package Bar;

sub new {
    say "Bar!";
    [];
}

package Foo;
    use base qw/Bar/;
    sub new {
      my $class = shift;
      say "Foo!";
      my $self  = $class->SUPER::new(@_);
      bless $self, $class;
      return $self;
    }

package main;
my $bletch = Foo->new;
say ref($bletch);  

__END__
Foo!
Bar!
Foo
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