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.

templates/parts/search-panel.php

@@ -1,6 +1,9 @@
 <?php
 /**
- * Global search panel (desktop + mobile).
+ * Footer tabbar / shell search overlay (NOT the top-nav zibll slide).
+ *
+ * Top navigation uses templates/parts/navbar-search.php (.navbar-search) for
+ * layouts 1/3 and remote menu_search for layout 2.
  *
  * DOM contracts for assets/js/core/search.js and footer-tabbar search tab:
  * - #tabbar-search-overlay (also #nav-search-panel for shell config)