feat(ui): refine home and private room navigation

Replace the floating bottom navigation with a full-width tab bar. Add splash press feedback and a neutral private room background.

src/app/splash/splash-screen.tsx

@@ -40,6 +40,10 @@ export function SplashScreen() {
     navigator.push(ROUTES.privateRoom, { scroll: false });
   };
 
+  const handleOpenSplash = () => {
+    navigator.push(ROUTES.splash, { scroll: false });
+  };
+
   useEffect(() => {
     pwaUtil.prepareInstallPrompt();
   }, []);
@@ -69,9 +73,9 @@ export function SplashScreen() {
           </p>
         </div>
         <AppBottomNav
-          activeItem={null}
+          activeItem="chat"
           variant="dark"
-          onChatClick={handleStartChat}
+          onChatClick={handleOpenSplash}
           onPrivateRoomClick={handleOpenPrivateRoom}
         />
       </div>