Improve menu category selection when scrolling to bottom

Automatically select the last category when the user scrolls to the bottom of the menu list.

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude <noreply@anthropic.com>

src/shared/ui/menu/index.tsx

@@ -218,8 +218,22 @@ export const Menu = ({
   const menuListScroll = () => {
     if (isButtonScrolling.current) return;
 
-    const scrollTop = scrollRef.current?.scrollTop || 0;
+    if (!scrollRef.current) return;
-    const currentIndex = getCurrentCategoryIndex(scrollTop);
+
+    const scrollTop = scrollRef.current.scrollTop;
+    const scrollHeight = scrollRef.current.scrollHeight;
+    const clientHeight = scrollRef.current.clientHeight;
+
+    // 스크롤이 맨 밑에 도달했는지 확인 (약간의 오차 허용)
+    const isAtBottom = scrollHeight - scrollTop - clientHeight < 1;
+
+    let currentIndex: number;
+    if (isAtBottom) {
+      // 맨 밑이면 마지막 카테고리 선택
+      currentIndex = buttonRefs.current.length - 1;
+    } else {
+      currentIndex = getCurrentCategoryIndex(scrollTop);
+    }
 
     if (currentIndex !== shortBtnIdx) {
       setShortBtnIdx(currentIndex);