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/README.md

@@ -25,7 +25,7 @@ src/
 │   ├── messages/         # Message feed, search, review, detail modal
 │   ├── live/             # Voice connection, music player, recordings
 │   ├── dashboard/        # Stats, users, channels overview
-│   └── mascot/           # AI chatbot
+│   └── chatbot/          # AI chatbot
 ├── lib/
 │   ├── api/              # Fetch-based API client (all BE endpoints)
 │   ├── ws/               # WebSocket client + React context