fix(menu): prevent mobile dropdown click from auto-focusing search

tests/mobile-menu-focus.spec.ts

@@ -0,0 +1,21 @@
+import { test, expect } from "@playwright/test";
+
+test("clicking mobile hamburger does not focus the sidebar search input", async ({
+  page,
+}) => {
+  await page.setViewportSize({ width: 375, height: 812 });
+  await page.goto("/", { waitUntil: "load" });
+
+  const menuButton = page.locator(".hextra-hamburger-menu");
+  await expect(menuButton).toBeVisible();
+
+  const sidebarSearchInput = page
+    .locator(".hextra-sidebar-container .hextra-search-input")
+    .first();
+  await expect(sidebarSearchInput).toBeVisible();
+
+  await menuButton.click();
+
+  await expect(menuButton).toHaveAttribute("aria-expanded", "true");
+  await expect(sidebarSearchInput).not.toBeFocused();
+});