chore(lint): biome cleanup across services — format, sort imports, drop unused

- discord-gateway: 74 lint errors -> 0 (format, import sorting, unused
  imports/vars, dead breath var)
- backend: format + sort imports (11 warnings left: noExplicitAny)
- frontend: remove unused imports, drop dead breathing var, fix
  useExhaustiveDependencies (scroll keyed on messages), a11y biome-ignore
  for drag surface + stopPropagation container (mouse-only gestures)
- remaining warnings are false positives: index keys on static lists,
  <img> in static export (next/image unsupported), noExplicitAny

tsc --noEmit clean on all 3 services; vitest green (60+36).

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

@@ -10,11 +10,7 @@ import { chatRequestSchema } from "./chatbot.schema.js";
 export function createChatbotRouter(): Router {
   const router = express.Router();
 
-  router.post(
-    "/chat",
-    validateBody(chatRequestSchema),
-    handleChatbotChat,
-  );
+  router.post("/chat", validateBody(chatRequestSchema), handleChatbotChat);
   router.get("/chat/history", getChatbotHistory);
   router.delete("/chat/history", clearChatbotHistory);