Responsive Sticky E-commerce Header & Nav Bar

<header class="sticky z-40 bg-white/80 border-neutral-200 border-b top-0 backdrop-blur">
      <div class="mx-auto max-w-7xl px-4 sm:px-6 lg:px-8">
        <div class="flex h-16 items-center justify-between">
          <!-- Mobile menu button -->
          <button id="openMenu" class="inline-flex items-center justify-center rounded-md p-2 text-neutral-600 hover:text-black hover:bg-neutral-100 focus:outline-none focus:ring-2 focus:ring-neutral-300 lg:hidden" aria-label="Open menu">
            <svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" data-lucide="menu" class="lucide lucide-menu h-6 w-6"><path d="M4 5h16" class=""></path><path d="M4 12h16" class=""></path><path d="M4 19h16" class=""></path></svg>
          </button>

          <!-- Brand -->
          <a href="#" class="flex-1 lg:flex-none text-center">
            <span class="text-2xl sm:text-3xl tracking-tight font-semibold">CERENZA</span>
          </a>

          <!-- Actions -->
          <div class="flex flex-1 items-center justify-end gap-4">
            <button class="p-2 rounded-md hover:bg-neutral-100" aria-label="Search">
              <svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" data-lucide="search" class="lucide lucide-search h-5 w-5"><path d="m21 21-4.34-4.34" class=""></path><circle cx="11" cy="11" r="8" class=""></circle></svg>
            </button>
            <button class="hidden sm:inline-flex p-2 rounded-md hover:bg-neutral-100" aria-label="Account">
              <svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" data-lucide="user" class="lucide lucide-user h-5 w-5"><path d="M19 21v-2a4 4 0 0 0-4-4H9a4 4 0 0 0-4 4v2" class=""></path><circle cx="12" cy="7" r="4" class=""></circle></svg>
            </button>
            <button class="hidden sm:inline-flex p-2 rounded-md hover:bg-neutral-100" aria-label="Favorites">
              <svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" data-lucide="star" class="lucide lucide-star h-5 w-5"><path d="M11.525 2.295a.53.53 0 0 1 .95 0l2.31 4.679a2.123 2.123 0 0 0 1.595 1.16l5.166.756a.53.53 0 0 1 .294.904l-3.736 3.638a2.123 2.123 0 0 0-.611 1.878l.882 5.14a.53.53 0 0 1-.771.56l-4.618-2.428a2.122 2.122 0 0 0-1.973 0L6.396 21.01a.53.53 0 0 1-.77-.56l.881-5.139a2.122 2.122 0 0 0-.611-1.879L2.16 9.795a.53.53 0 0 1 .294-.906l5.165-.755a2.122 2.122 0 0 0 1.597-1.16z" class=""></path></svg>
            </button>
            <button class="inline-flex p-2 rounded-md hover:bg-neutral-100" aria-label="Bag">
              <svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" data-lucide="shopping-bag" class="lucide lucide-shopping-bag h-5 w-5"><path d="M16 10a4 4 0 0 1-8 0" class=""></path><path d="M3.103 6.034h17.794" class=""></path><path d="M3.4 5.467a2 2 0 0 0-.4 1.2V20a2 2 0 0 0 2 2h14a2 2 0 0 0 2-2V6.667a2 2 0 0 0-.4-1.2l-2-2.667A2 2 0 0 0 17 2H7a2 2 0 0 0-1.6.8z" class=""></path></svg>
            </button>
          </div>
        </div>
      </div>

      <!-- Category Nav -->
      <nav class="border-neutral-200 border-t">
        <div class="mx-auto max-w-7xl px-4 sm:px-6 lg:px-8">
          <ul class="flex gap-6 overflow-x-auto py-3 text-sm text-neutral-700">
            <li class=""><a class="hover:text-black whitespace-nowrap" href="#">Haute Couture</a></li>
            <li class=""><a class="hover:text-black whitespace-nowrap" href="#">Ready-to-Wear</a></li>
            <li class=""><a class="hover:text-black whitespace-nowrap" href="#">High Jewelry</a></li>
            <li class=""><a class="hover:text-black whitespace-nowrap" href="#">Fine Jewelry</a></li>
            <li class=""><a class="hover:text-black whitespace-nowrap" href="#">Watches</a></li>
            <li class=""><a class="hover:text-black whitespace-nowrap" href="#">Eyewear</a></li>
            <li class=""><a class="hover:text-black whitespace-nowrap" href="#">Fragrance</a></li>
            <li class=""><a class="hover:text-black whitespace-nowrap" href="#">Beauty</a></li>
            <li class=""><a class="hover:text-black whitespace-nowrap" href="#">Skincare</a></li>
            <li class=""><a class="hover:text-black whitespace-nowrap" href="#">About</a></li>
          </ul>
        </div>
      </nav>
    </header>