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/private-room/private-room-screen.tsx

@@ -80,7 +80,7 @@ export function PrivateRoomScreen() {
   };
 
   return (
-    <MobileShell background="#fff7ed">
+    <MobileShell background="#f3f4f2">
       <main className={styles.shell}>
         <div className={styles.backgroundGlowOne} />
         <div className={styles.backgroundGlowTwo} />
@@ -186,7 +186,7 @@ export function PrivateRoomScreen() {
 
         <AppBottomNav
           activeItem="privateRoom"
-          onChatClick={() => navigator.openChat({ replace: false })}
+          onChatClick={() => navigator.push(ROUTES.splash, { scroll: false })}
           onPrivateRoomClick={() => undefined}
         />