PM2 cluster deploy + Redis caching + Nginx gzip + UI polish

- PM2 v6: 2x API cluster + 1x web, zero-downtime reload
- Redis cache: 30s TTL on GET /tasks, X-Cache header
- Nginx gzip compression
- Mobile touch targets 44px
- Czech diacritics throughout UI
- TaskModal slide-up animation
- StatusBadge color dots
- GroupSelector emoji icons

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

apps/tasks/components/BottomNav.tsx

@@ -0,0 +1,72 @@
+"use client";
+
+import Link from "next/link";
+import { usePathname } from "next/navigation";
+
+const NAV_ITEMS = [
+  {
+    href: "/tasks",
+    label: "Ukoly",
+    icon: (
+      <svg className="w-6 h-6" fill="none" viewBox="0 0 24 24" stroke="currentColor" strokeWidth={1.5}>
+        <path strokeLinecap="round" strokeLinejoin="round" d="M9 5H7a2 2 0 00-2 2v12a2 2 0 002 2h10a2 2 0 002-2V7a2 2 0 00-2-2h-2M9 5a2 2 0 002 2h2a2 2 0 002-2M9 5a2 2 0 012-2h2a2 2 0 012 2m-6 9l2 2 4-4" />
+      </svg>
+    ),
+  },
+  {
+    href: "/calendar",
+    label: "Kalendar",
+    icon: (
+      <svg className="w-6 h-6" fill="none" viewBox="0 0 24 24" stroke="currentColor" strokeWidth={1.5}>
+        <path strokeLinecap="round" strokeLinejoin="round" d="M8 7V3m8 4V3m-9 8h10M5 21h14a2 2 0 002-2V7a2 2 0 00-2-2H5a2 2 0 00-2 2v12a2 2 0 002 2z" />
+      </svg>
+    ),
+  },
+  {
+    href: "/chat",
+    label: "Chat",
+    icon: (
+      <svg className="w-6 h-6" fill="none" viewBox="0 0 24 24" stroke="currentColor" strokeWidth={1.5}>
+        <path strokeLinecap="round" strokeLinejoin="round" d="M8 12h.01M12 12h.01M16 12h.01M21 12c0 4.418-4.03 8-9 8a9.863 9.863 0 01-4.255-.949L3 20l1.395-3.72C3.512 15.042 3 13.574 3 12c0-4.418 4.03-8 9-8s9 3.582 9 8z" />
+      </svg>
+    ),
+  },
+  {
+    href: "/settings",
+    label: "Nastaveni",
+    icon: (
+      <svg className="w-6 h-6" fill="none" viewBox="0 0 24 24" stroke="currentColor" strokeWidth={1.5}>
+        <path strokeLinecap="round" strokeLinejoin="round" d="M10.325 4.317c.426-1.756 2.924-1.756 3.35 0a1.724 1.724 0 002.573 1.066c1.543-.94 3.31.826 2.37 2.37a1.724 1.724 0 001.066 2.573c1.756.426 1.756 2.924 0 3.35a1.724 1.724 0 00-1.066 2.573c.94 1.543-.826 3.31-2.37 2.37a1.724 1.724 0 00-2.573 1.066c-.426 1.756-2.924 1.756-3.35 0a1.724 1.724 0 00-2.573-1.066c-1.543.94-3.31-.826-2.37-2.37a1.724 1.724 0 00-1.066-2.573c-1.756-.426-1.756-2.924 0-3.35a1.724 1.724 0 001.066-2.573c-.94-1.543.826-3.31 2.37-2.37.996.608 2.296.07 2.572-1.065z" />
+        <path strokeLinecap="round" strokeLinejoin="round" d="M15 12a3 3 0 11-6 0 3 3 0 016 0z" />
+      </svg>
+    ),
+  },
+];
+
+export default function BottomNav() {
+  const pathname = usePathname();
+
+  return (
+    <nav className="bottom-nav fixed bottom-0 left-0 right-0 z-50 bg-white/90 dark:bg-gray-950/90 backdrop-blur-lg border-t border-gray-200 dark:border-gray-800 safe-area-bottom">
+      <div className="flex items-center justify-around h-16 max-w-lg mx-auto px-2">
+        {NAV_ITEMS.map((item) => {
+          const isActive = pathname?.startsWith(item.href);
+          return (
+            <Link
+              key={item.href}
+              href={item.href}
+              className={`flex flex-col items-center justify-center gap-0.5 flex-1 h-full min-w-[64px] min-h-[48px] rounded-lg transition-colors ${
+                isActive
+                  ? "text-blue-600 dark:text-blue-400"
+                  : "text-gray-400 dark:text-gray-500 hover:text-gray-600 dark:hover:text-gray-300"
+              }`}
+            >
+              {item.icon}
+              <span className="text-[10px] font-medium leading-none">{item.label}</span>
+            </Link>
+          );
+        })}
+      </div>
+    </nav>
+  );
+}