refactor: rename mascot to chatbot across entire codebase

- Backend: mascot-chat module → chatbot, routes /mascot/chat → /chat
- Shared schema: pgMascotChatMessagesTable → pgChatbotMessagesTable
- Frontend: MascotProvider/useMascot → ChatbotProvider/useChatbot
- Gateway schema: update exports to match shared schema
- Docs: update all .md references (CLAUDE.md, README, specs, plans)
- All API routes, controller names, service classes, types renamed

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

services/frontend/src/lib/api/chatbot.ts

@@ -3,9 +3,9 @@ import { api } from "./client";
 
 export const chatbotApi = {
   send: (message: string) =>
-    api.post<ChatbotResponse>("/api/mascot/chat", { message }),
+    api.post<ChatbotResponse>("/api/chat", { message }),
 
-  getHistory: () => api.get<ChatHistoryMessage[]>("/api/mascot/chat/history"),
+  getHistory: () => api.get<ChatHistoryMessage[]>("/api/chat/history"),
 
-  clearHistory: () => api.delete<{ ok: boolean }>("/api/mascot/chat/history"),
+  clearHistory: () => api.delete<{ ok: boolean }>("/api/chat/history"),
 };