$str =~ m/.../g in scalar context keeps track of its current position via pos($str), and $str =~ s/.../.../g resets pos($str).

You could something along these lines instead:

$post_message =~ s{\[\[([^]]+)\]\]}{process_match($1)}ge;

sub process_match {
   my $tmp = shift;
   if ($DB->table('Articles')->count( { article_title => $tmp } ) > 0)
+ {
      # return modified text here
   } else {
      return $tmp;  # unmodified text
   }
}
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