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/backend/src/modules/chatbot/chatbot.routes.ts

@@ -0,0 +1,22 @@
+import express, { type Router } from "express";
+import { validateBody } from "../../shared/middlewares/index.js";
+import {
+  clearChatbotHistory,
+  getChatbotHistory,
+  handleChatbotChat,
+} from "./chatbot.controller.js";
+import { chatRequestSchema } from "./chatbot.schema.js";
+
+export function createChatbotRouter(): Router {
+  const router = express.Router();
+
+  router.post(
+    "/chat",
+    validateBody(chatRequestSchema),
+    handleChatbotChat,
+  );
+  router.get("/chat/history", getChatbotHistory);
+  router.delete("/chat/history", clearChatbotHistory);
+
+  return router;
+}