Shouldn't
$#{@{$object_ref->{array_ref}}}
be
$#{$object_ref->{array_ref}}
(The last index of the array referenced by $object_ref->{array_ref}.)

By eliminating multiple instances of $object_ref->{array_ref},

foreach (0..$#{$object_ref->{array_ref}}) {
   printf("%d %s\n", $_, $object_ref->{array_ref}[$_]);
}
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might be more readable as

my $array = $object_ref->{array_ref};
foreach (0..$#$array) {
   printf("%d %s\n", $_, $array->[$_]);
}
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my $array = $object_ref->{array_ref};
foreach my $idx (0..$#$array) {
   foreach my $ele ($array->[$idx]) {
      printf("%d %s\n", $idx, $ele);
   }
}
[download]