feat: chat pagination — infinite scroll / load older messages

- Backend: cursor-based pagination via ?before=<ISO timestamp>
- Frontend: auto-load when scrolling to top (<60px), spinner + manual 'Загрузить ещё' button
- Poll merge: preserves older history when new messages arrive from polling
- hasMoreMsgs flag: shown only when exactly 50 msgs returned (more may exist)

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

src/lib/api.ts

@@ -333,8 +333,10 @@ export const api = {
   chat: {
     listRooms: (slug: string) =>
       req<ChatRoom[]>('GET', `/api/hotels/${slug}/chat/rooms`),
-    getMessages: (slug: string, roomId: string, limit = 50) =>
-      req<ChatMessage[]>('GET', `/api/hotels/${slug}/chat/rooms/${roomId}/messages?limit=${limit}`),
+    getMessages: (slug: string, roomId: string, limit = 50, before?: string) => {
+      const qs = before ? `?limit=${limit}&before=${encodeURIComponent(before)}` : `?limit=${limit}`
+      return req<ChatMessage[]>('GET', `/api/hotels/${slug}/chat/rooms/${roomId}/messages${qs}`)
+    },
     sendMessage: (slug: string, roomId: string, text: string, attachmentUrl?: string) =>
       req<ChatMessage>('POST', `/api/hotels/${slug}/chat/rooms/${roomId}/messages`, { text, ...(attachmentUrl ? { attachment_url: attachmentUrl } : {}) }),
     uploadImage: async (file: File): Promise<{ url: string }> => {