Simplify the logic for determining `isset( $this->query['s'] )` after [28612], and don't limit this logic to just the main query.

Props SergeyBiryukov.
Fixes #11330.

Built from https://develop.svn.wordpress.org/trunk@28623


git-svn-id: http://core.svn.wordpress.org/trunk@28444 1a063a9b-81f0-0310-95a4-ce76da25c4cd