How to achieve post_status__not_in?

Unfortunately there is no post_status__not_in query argument, but you can simply query for all statuses other than trash & draft:

$stati = array_keys( get_post_stati() );
unset( $stati['trash'], $stati['draft'] );
$stati = array_flip( $stati );

$query->set( 'post_status', $stati );

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