refactor: comprehensive codebase cleanup and architecture hardening

- Sprint 1 (Quick Wins): Remove dead analytics modules, fix 4 unresolved
  imports, replace 3 console.warn with logger, remove mock-crc import
- Sprint 2 (Architecture): Create MascotChatRepository, AnalysisRepository,
  3 Zod schemas (mascot-chat, analysis, voice), deduplicate error classes,
  move 3 SQL queries from routes to repository
- Sprint 3 (Complexity): Replace 7 any types with proper interfaces,
  extract 6 helpers from prepareMediaMessage (CC 85 -> ~15)
- Sprint 4 (Config): Remove 22 dead env vars from .env, add 30 missing
  vars to .env.example, standardize naming

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

services/discord-gateway/README.md

@@ -260,7 +260,7 @@ On SIGINT/SIGTERM/uncaughtException/unhandledRejection:
 ### Shared Infrastructure (9 files)
 - `src/shared/config/config.ts`
 - `src/shared/database/` (5 files)
-- `src/shared/errors/errors.ts`
+- `@bete/shared/errors` (shared package)
 - `src/shared/logger/logger.ts`
 - `src/shared/logger/serialization.ts`
 - `src/shared/utils/retry.ts`