fix(nav): focus search input when mobile menu opens (#523)

Code review of #518 found that moving the search box to the top of the
mobile menu (visually) left keyboard/screen-reader focus order
unchanged: Tab still traverses the whole nav list before reaching
search, since DOM order wasn't touched, only CSS position. That's now
inconsistent with the new visual order.

Focus the search input as soon as the mobile menu opens, matching its
new position at the top. The listener runs after Just the Docs' own
(head_custom.html loads after just-the-docs.js), so nav-open has
already been toggled by the time it checks. Confirmed this doesn't
prematurely expand the search results UI (that's gated on non-empty
input, unaffected by focus alone) and doesn't affect desktop, where
the menu button is hidden.

Verified via headless Chromium: menu open -> focus lands on
#search-input; typing still triggers results normally; desktop
unaffected.

Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>

Author: gkorland

_includes/head_custom.html

@@ -53,6 +53,38 @@
 }
 </style>
 
+<!-- Mobile menu: move focus to search when the menu opens. The search box
+     now appears visually at the top of the mobile menu (see above), but
+     keyboard/screen-reader focus order still follows the unchanged DOM
+     order (nav links, then search). Moving focus to the search input on
+     open keeps focus order consistent with what's visually first, without
+     changing tab order for anyone not using the menu button.
+
+     Ordering notes for future maintainers:
+     - This listener is attached after Just the Docs' own (head_custom.html
+       is included after just-the-docs.js, see theme's _includes/head.html),
+       so nav-open has already been toggled by the time it runs.
+     - The check is intentionally synchronous (no setTimeout/microtask
+       deferral): iOS Safari only shows the on-screen keyboard for a
+       programmatic focus() call made synchronously within the original
+       click handler. Deferring the check would move focus silently
+       without opening the keyboard on iOS Safari, defeating the point of
+       this fix for a large share of mobile users. -->
+<script>
+document.addEventListener("DOMContentLoaded", function () {
+  var menuButton = document.getElementById("menu-button");
+  var mainHeader = document.getElementById("main-header");
+  var searchInput = document.getElementById("search-input");
+  if (!menuButton || !mainHeader || !searchInput) return;
+
+  menuButton.addEventListener("click", function () {
+    if (mainHeader.classList.contains("nav-open")) {
+      searchInput.focus();
+    }
+  });
+});
+</script>
+
 <!-- Sticky right-side Table of Contents -->
 <style>
 .toc-sidebar {