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/js/core/search.js

@@ -291,19 +291,20 @@
 
     document.querySelectorAll(".main-search-btn, .nav-search-toggle, [data-aksrt-open-search]").forEach(function (btn) {
       btn.addEventListener("click", function (e) {
+        // Top bar uses zibll .navbar-search slide — skip tabbar overlay.
+        var tgt = btn.getAttribute("data-target") || "";
+        if (tgt.indexOf("navbar-search") !== -1 || tgt.indexOf("main-search") !== -1) {
+          return;
+        }
         e.preventDefault();
         setOpen(true);
       });
     });
 
-    // Zibll-compatible data-toggle-class for .navbar-search
-    document.addEventListener("click", function (e) {
-      var toggle = e.target.closest('[data-toggle-class][data-target=".navbar-search"], [data-toggle-class][data-target=".main-search"]');
-      if (!toggle) return;
-      e.preventDefault();
-      var isOpen = mobileOverlay && !mobileOverlay.hasAttribute("hidden");
-      setOpen(!isOpen);
-    });
+    // Top-nav .navbar-search is toggled by aksrt-runtime (data-toggle-class="show").
+    // Do NOT redirect those clicks into the footer tabbar overlay.
+    // Only open tabbar overlay for explicit main-search-btn without .navbar-search target
+    // (handled above via .main-search-btn listeners).
 
     if (historyClear) {
       historyClear.addEventListener("click", function () {