feat(navigation): add favorite entry and Menu tab

src/app/_components/core/app-bottom-nav.tsx

@@ -1,10 +1,10 @@
 "use client";
 
-import { Camera, MessageCircle } from "lucide-react";
+import { Camera, Menu as MenuIcon, MessageCircle } from "lucide-react";
 
 import styles from "./app-bottom-nav.module.css";
 
-export type AppBottomNavItem = "chat" | "privateZoom";
+export type AppBottomNavItem = "chat" | "privateZoom" | "menu";
 export type AppBottomNavVariant = "warm" | "dark";
 
 export interface AppBottomNavProps {
@@ -13,6 +13,7 @@ export interface AppBottomNavProps {
   privateZoomLabel: string;
   onChatClick: () => void;
   onPrivateZoomClick: () => void;
+  onMenuClick: () => void;
 }
 
 export function AppBottomNav({
@@ -21,6 +22,7 @@ export function AppBottomNav({
   privateZoomLabel,
   onChatClick,
   onPrivateZoomClick,
+  onMenuClick,
 }: AppBottomNavProps) {
   return (
     <nav className={getRootClass(variant)} aria-label="Primary navigation">
@@ -46,6 +48,17 @@ export function AppBottomNav({
         <Camera size={20} aria-hidden="true" />
         <span>{privateZoomLabel}</span>
       </button>
+      <button
+        type="button"
+        data-analytics-key="navigation.menu"
+        data-analytics-label="Menu navigation"
+        className={getButtonClass(activeItem === "menu")}
+        aria-current={activeItem === "menu" ? "page" : undefined}
+        onClick={onMenuClick}
+      >
+        <MenuIcon size={20} aria-hidden="true" />
+        <span>Menu</span>
+      </button>
     </nav>
   );
 }