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/frontend/src/components/messages/search-overlay.tsx

@@ -4,7 +4,6 @@ import { Search, X } from "lucide-react";
 import { useEffect, useRef, useState } from "react";
 import { useMessageSearch } from "@/hooks";
 import { getMessageChannelLabel, renderMessageContent } from "@/lib/format";
-import type { MessageRecord } from "@/lib/types";
 
 interface SearchOverlayProps {
   open: boolean;