I think the following will do the trick:

foreach my $dir (sort { length($b) <=> length($a) } keys %hash) {
   next unless $dir =~ m{^(.*)/[^/]*$};
   my $parent = $1;
   next unless exists $hash{$parent};
   $hash{$parent}{dir} += $hash{$dir}{dir};
}
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The sort is essential in propagating the changes towards the root.