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.

assets/css/frontend/nav.css

@@ -3,6 +3,7 @@
 @import url("nav/zib-mobile-navbar.css");
 @import url("nav/zib-senior-submenu.css");
 @import url("nav/zib-utilities.css");
+@import url("nav/zib-search-box.css");
 @import url("nav/header-menu-buttons.css");
 @import url("nav/header-userbox.css");
 @import url("nav/dark-mode-submenu.css");