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/modules/ai-moderation/index.ts

@@ -1,12 +1,11 @@
-export { startPendingAIAnalysisWorker } from "./aiAnalyzer.js";
-export { runModerationAnalysis } from "./moderationOrchestrator.js";
-export { buildSystemPrompt } from "./moderationPrompt.js";
-export { sanitizeDiscordTokens } from "./discordTokens.js";
-
 // ── Single-pass LLM pipeline exports ─────────────────────────────────────
 export type {
   AnalysisInput,
   AnalysisResult,
-  WorkerConfig,
   MessageBatch,
+  WorkerConfig,
 } from "./ai-analysis-worker.js";
+export { startPendingAIAnalysisWorker } from "./aiAnalyzer.js";
+export { sanitizeDiscordTokens } from "./discordTokens.js";
+export { runModerationAnalysis } from "./moderationOrchestrator.js";
+export { buildSystemPrompt } from "./moderationPrompt.js";