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/shared/redis/index.ts

@@ -1,4 +1,6 @@
 import { randomUUID } from "node:crypto";
+import Redis from "ioredis";
+import { config } from "../config/index.js";
 import {
   BACKEND_COMMAND,
   BACKEND_COMMAND_REPLY_PREFIX,
@@ -6,8 +8,6 @@ import {
   type CommandReply,
 } from "../index.js";
 import { createChildLogger } from "../logger/index.js";
-import Redis from "ioredis";
-import { config } from "../config/index.js";
 
 const logger = createChildLogger("redis.command-channel");