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/dashboard/dashboard.routes.ts

@@ -1,6 +1,6 @@
-import { createChildLogger } from "@/shared/logger/index";
 import type { Request, Response, Router } from "express";
 import express from "express";
+import { createChildLogger } from "@/shared/logger/index";
 import { asyncHandler } from "../../shared/middlewares/index.js";
 import { dashboardService } from "./dashboard.service.js";