feat: 채팅 내역 저장하기 구현

src/components/header/SubHeader.tsx

@@ -24,6 +24,7 @@ const SubHeader = ({
   const isChatPage = pathname === "/chat";
   const isFirstQuestionPage = currentPage === 1;
   const mode = state?.mode;
+  const chatId = state?.id;
 
   const handleGoBack = () => {
     if (isProgressPage && !isFirstQuestionPage) {
@@ -45,6 +46,10 @@ const SubHeader = ({
   const handleCancel = () => setIsLeaveChatModalOpen(false);
 
   const handleConfirm = () => {
+    if (chatId) {
+      sessionStorage.removeItem(`chatMessages_${chatId}`);
+    }
+
     setIsLeaveChatModalOpen(false);
     navigate("/");
   };

src/pages/Chat.tsx

@@ -20,7 +20,7 @@ interface ChatResponse {
 
 const Chat = () => {
   const { state } = useLocation();
-  const { mbti, mode, id } = state;
+  const { mbti, mode, id = Date.now().toString() } = state;
 
   const [messages, setMessages] = useState<Message[]>([]);
   const [input, setInput] = useState("");
@@ -30,11 +30,21 @@ const Chat = () => {
   const chatTitle = `${mbti}와 대화`;
   const assistantInfo = mbti;
   const assistantImgUrl = pickMbtiImage(assistantInfo);
+  const storageKey = `chatMessages_${id}`;
 
   useEffect(() => {
     bottomRef.current?.scrollIntoView({ behavior: "smooth" });
   }, [messages, isOpen]);
 
+  useEffect(() => {
+    const stored = sessionStorage.getItem(storageKey);
+    if (stored) setMessages(JSON.parse(stored));
+  }, [storageKey]);
+
+  useEffect(() => {
+    sessionStorage.setItem(storageKey, JSON.stringify(messages));
+  }, [messages, storageKey]);
+
   const handleToggleTips = () => {
     const nextAction = !isOpen;