[Refactor] 과제 api 연결 및 바뀐 dto 반영

apps/client/constants/navMenu.ts

@@ -11,7 +11,7 @@ export const navMenu = [
     name: "나의 스터디",
     items: [
       {
-        href: "/my-assignment",
+        href: "my-assignment",
         imageUrl: folderImageUrl,
         alt: "folder-icon",
         name: "나의 과제",

packages/ui/src/components/NavItem/index.tsx

@@ -46,8 +46,11 @@ const NavItem = ({ href, imageUrl, alt, name, items }: NavItemProps) => {
     }
   };
 
+  const currentPath = `/${segment.join("/")}`;
+
   const navItemType =
-    (!segment[1] && `${segment[0]}` === href) || `/${segment[0]}` === href
+    (currentPath === href && !segment[1] && `${segment[0]}` === href) ||
+    (currentPath === href && `/${segment[0]}` === href)
       ? "active"
       : "inactive";