Why won’t draft listings appear for non-admins?

There is indeed processing in WP_Query which might prevent posts from displaying if they are not simply public.

Since there are several conditions there it is a little hard to guess why it fails in your specific case. It might be issue with how permissions are setup or some edge case (which querying for non-public posts is full of).

Hata!: SQLSTATE[HY000] [1045] Access denied for user 'divattrend_liink'@'localhost' (using password: YES)