메뉴 및 슬라이드 메뉴 다국어화

- MenuItems에 영문 메뉴명(menuNameEng) 추가
- MenuCategory 컴포넌트에 i18n 적용하여 언어별 메뉴 표시
- SlideMenu 컴포넌트 다국어 지원 추가
- ko.json, en.json에 slideMenu 번역 키 추가

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

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

src/entities/menu/ui/menu-category.tsx

@@ -5,6 +5,8 @@ import { UserFavorite } from '@/entities/user/model/types';
 import { RefObject, useEffect, useState } from 'react';
 import { useLocation } from 'react-router';
 import { MenuItem } from '../model/types';
+import { useTranslation } from 'react-i18next';
+import { MenuItems } from '@/entities/common/model/constant';
 
 export interface MenuCategoryProps {
   menuId?: number;
@@ -32,6 +34,7 @@ export const MenuCategory = ({
   itemIndex
 }: MenuCategoryProps) => {
   const { navigate } = useNavigate();
+  const { i18n } = useTranslation();
   // const location = useLocation();
 
   const [favoriteItems, setFavoriteItems] = useState<Array<UserFavorite>>([]);
@@ -115,29 +118,33 @@ export const MenuCategory = ({
     let rs = [];
     if(subMenu){
       for(let i=0;i<subMenu.length;i++){
+        const displayName = i18n.language === 'en' && subMenu[i]?.menuNameEng
+          ? subMenu[i]?.menuNameEng
+          : subMenu[i]?.menuName;
+
         if(!!editMode && subMenu[i] && subMenu[i]?.menuId){
           rs.push(
             <li
               key={ `menu-item-key-${menuId}-${i}` }
               onClick={ () => onClickToNavigate(subMenu[i]?.programPath) }
             >
-              <span>{ subMenu[i]?.menuName }</span>
+              <span>{ displayName }</span>
               <div className="check_box_scrap">
-                <input 
+                <input
                   id={ `menu-item-checkbox-${subMenu[i]?.menuId}-${i}` }
                   className="checkbox"
                   type="checkbox"
                   checked={ menuIds.includes(subMenu[i]?.menuId)? true: false }
                   onChange={ (e) => favoriteSetting(
-                    e.target.checked, 
+                    e.target.checked,
                     subMenu[i]?.menuId,
                     subMenu[i]?.menuName,
-                    subMenu[i]?.menuNameEng, 
+                    subMenu[i]?.menuNameEng,
                     subMenu[i]?.iconFilePath,
                     subMenu[i]?.programPath,
                   )}
                 />
-                <label 
+                <label
                   className="gtr"
                   htmlFor={ `menu-item-checkbox-${subMenu[i]?.menuId}-${i}` }
                 ></label>
@@ -150,16 +157,20 @@ export const MenuCategory = ({
             <li
               key={ `menu-item-key-${i}` }
               onClick={ () => onClickToNavigate(subMenu[i]?.programPath) }
-            >{ subMenu[i]?.menuName }</li>
+            >{ displayName }</li>
           );
         }
-        
+
       }
     }
-    
+
     return rs;
   };
 
+  const displayCategoryName = i18n.language === 'en'
+    ? MenuItems.find(item => item.menuId === menuId)?.menuNameEng || menuName
+    : menuName;
+
   return (
     <>
       <div
@@ -172,7 +183,7 @@ export const MenuCategory = ({
       >
         <div className="category-header">
           <div className={ 'category-icon ' + iconFilePath }></div>
-          <span>{ menuName }</span>
+          <span>{ displayCategoryName }</span>
         </div>
         <ul className="category-items">
         { getMenuItems() }