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/discord-gateway/src/app/bootstrap.ts

@@ -1,8 +1,8 @@
-import { ConfigError, DatabaseError } from "@/shared/errors/index";
-import { createChildLogger } from "@/shared/logger/index";
 import { Client } from "discord.js-selfbot-v13";
 import { inArray, lt } from "drizzle-orm";
 import type { NodePgDatabase } from "drizzle-orm/node-postgres";
+import { ConfigError, DatabaseError } from "@/shared/errors/index";
+import { createChildLogger } from "@/shared/logger/index";
 import { startPendingAIAnalysisWorker } from "../modules/ai-moderation/aiAnalyzer.js";
 import { registerChannelTopicCapture } from "../modules/channel-topic/index.js";
 import { CommandHandler } from "../modules/command-handler/commandHandler.js";