[RAPID] feat: 메신저 기능 구현 (Socket.IO 실시간 채팅)

- DB: messenger_rooms/participants/messages/reactions/files 테이블 생성
- Backend: REST API 9개 엔드포인트 + Socket.IO 실시간 핸들러
- Frontend: Gmail 스타일 FAB + 모달, 채팅방 목록, 채팅 패널
- 기능: DM/그룹/채널, 파일 첨부, 이모지 리액션, 멘션, 스레드
- 알림: 토스트 on/off 토글, FAB 읽지 않은 배지

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

frontend/contexts/MessengerContext.tsx

@@ -0,0 +1,76 @@
+"use client";
+
+import React, { createContext, useContext, useState, useCallback, useEffect } from "react";
+
+interface MessengerContextValue {
+  isOpen: boolean;
+  selectedRoomId: string | null;
+  unreadCount: number;
+  notificationEnabled: boolean;
+  openMessenger: (roomId?: string) => void;
+  closeMessenger: () => void;
+  selectRoom: (roomId: string) => void;
+  setUnreadCount: (count: number) => void;
+  toggleNotification: () => void;
+}
+
+const MessengerContext = createContext<MessengerContextValue | undefined>(undefined);
+
+export function MessengerProvider({ children }: { children: React.ReactNode }) {
+  const [isOpen, setIsOpen] = useState(false);
+  const [selectedRoomId, setSelectedRoomId] = useState<string | null>(null);
+  const [unreadCount, setUnreadCount] = useState(0);
+  const [notificationEnabled, setNotificationEnabled] = useState(true);
+
+  useEffect(() => {
+    const stored = localStorage.getItem("messenger_notification");
+    if (stored !== null) {
+      setNotificationEnabled(stored === "true");
+    }
+  }, []);
+
+  const openMessenger = useCallback((roomId?: string) => {
+    setIsOpen(true);
+    if (roomId) setSelectedRoomId(roomId);
+  }, []);
+
+  const closeMessenger = useCallback(() => {
+    setIsOpen(false);
+  }, []);
+
+  const selectRoom = useCallback((roomId: string) => {
+    setSelectedRoomId(roomId);
+  }, []);
+
+  const toggleNotification = useCallback(() => {
+    setNotificationEnabled((prev) => {
+      const next = !prev;
+      localStorage.setItem("messenger_notification", String(next));
+      return next;
+    });
+  }, []);
+
+  return (
+    <MessengerContext.Provider
+      value={{
+        isOpen,
+        selectedRoomId,
+        unreadCount,
+        notificationEnabled,
+        openMessenger,
+        closeMessenger,
+        selectRoom,
+        setUnreadCount,
+        toggleNotification,
+      }}
+    >
+      {children}
+    </MessengerContext.Provider>
+  );
+}
+
+export function useMessengerContext() {
+  const ctx = useContext(MessengerContext);
+  if (!ctx) throw new Error("useMessengerContext must be used within MessengerProvider");
+  return ctx;
+}