feat: 실시간 채팅 UI (STOMP 연동)

- ChatDialog: 히스토리 로드 + 실시간 송수신, 내 메시지 우측 정렬, 연결상태 표시
- lib/chatSocket: STOMP 클라이언트(브로커 ws, Bearer 인증, 자동 재연결)
- api/chat 히스토리, HomePage 스팟 채팅 버튼
- @stomp/stompjs 의존성 추가

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

src/lib/chatSocket.ts

@@ -0,0 +1,45 @@
+import { Client, type IMessage } from '@stomp/stompjs'
+import { tokenStore } from '@/lib/token'
+import type { ChatMessage } from '@/api/chat'
+
+function wsUrl(): string {
+  const base = import.meta.env.VITE_API_BASE_URL ?? 'http://localhost:8080'
+  // http(s) -> ws(s)
+  return base.replace(/^http/, 'ws') + '/ws'
+}
+
+/**
+ * 스팟 채팅용 STOMP 클라이언트.
+ * connect 후 스팟 토픽을 구독하고, send 로 메시지를 전송한다.
+ */
+export function createSpotChat(
+  spotId: number,
+  onMessage: (m: ChatMessage) => void,
+  onStatus?: (connected: boolean) => void,
+) {
+  const client = new Client({
+    brokerURL: wsUrl(),
+    connectHeaders: { Authorization: `Bearer ${tokenStore.get() ?? ''}` },
+    reconnectDelay: 3000,
+    onConnect: () => {
+      onStatus?.(true)
+      client.subscribe(`/topic/spots/${spotId}`, (msg: IMessage) => {
+        onMessage(JSON.parse(msg.body) as ChatMessage)
+      })
+    },
+    onDisconnect: () => onStatus?.(false),
+    onWebSocketClose: () => onStatus?.(false),
+  })
+
+  return {
+    activate: () => client.activate(),
+    deactivate: () => client.deactivate(),
+    send: (content: string) => {
+      client.publish({
+        destination: `/app/spots/${spotId}/chat`,
+        body: JSON.stringify({ content }),
+      })
+    },
+    isConnected: () => client.connected,
+  }
+}