feat(nav): deep 1:1 zibll search-box + navbar-search + newposts unify

Port aksrt_get_search_box/posts for menu_search and layout 1/3 slide;
unify publish switch; expand user-box admin row; CSS/JS remote-box parity.

inc/helpers/header/aksrt-header-mobile.php

@@ -77,7 +77,7 @@ if (!function_exists('aksrt_nav_mobile_content')) :
 			$top_btns .= '</a>';
 		}
 		if ($m_layout !== 'center' && !empty($ctx['search_enabled'])) {
-			$top_btns .= '<a href="javascript:;" class="toggle-radius main-search-btn" data-toggle-class data-target=".navbar-search" aria-label="'
+			$top_btns .= '<a href="javascript:;" class="toggle-radius main-search-btn" data-toggle-class="show" data-target=".navbar-search" aria-label="'
 				. esc_attr__('打开搜索', 'aksrt') . '"><i class="fas fa-search" aria-hidden="true"></i></a>';
 		}
 		if (function_exists('aksrt_get_translate_language_btn')) {