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/database/schema.ts

@@ -592,5 +592,4 @@ export type DbRetentionPolicyInsert =
 
 // Chatbot Messages
 export type ChatbotMessage = typeof chatbotMessagesTable.$inferSelect;
-export type ChatbotMessageInsert =
-  typeof chatbotMessagesTable.$inferInsert;
+export type ChatbotMessageInsert = typeof chatbotMessagesTable.$inferInsert;