Use Symfony Request for search module

Part of #1998638: [Meta] Refactor raw PHP variables (e.g $_SERVER, $_REQUEST, $_GET, $_POST) with Symfony Request object

Files that need converting are:

• core/modules/search/search.api.php
• core/modules/search/search.module
• core/modules/search/search.pages.inc
• core/modules/search/tests/modules/search_extra_type/search_extra_type.module