feat: Complete NestJS backend scaffold — 22 modules, 39 entities, WebSocket gateway

Full backend rewrite from Rust/Axum to NestJS/TypeScript.
- 22 feature modules (auth, servers, wipes, maps, plugins, players, console,
  chat, team, notifications, settings, schedules, analytics, alerts, status,
  store, webstore, admin, setup, migration, users, licenses)
- 39 TypeORM entities matching PostgreSQL schema (12 migrations)
- Common infrastructure: JWT/RBAC guards, decorators, exception filter
- NATS service with pub/sub/request-reply
- Socket.IO WebSocket gateway with NATS bridge
- Docker: NestJS Dockerfile + updated docker-compose.yml
- Zero compile errors (npx tsc --noEmit clean)

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

backend-nest/src/modules/chat/chat.module.ts

@@ -0,0 +1,13 @@
+import { Module } from '@nestjs/common';
+import { TypeOrmModule } from '@nestjs/typeorm';
+import { ChatController } from './chat.controller';
+import { ChatService } from './chat.service';
+import { ChatLog } from '../../entities/chat-log.entity';
+
+@Module({
+  imports: [TypeOrmModule.forFeature([ChatLog])],
+  controllers: [ChatController],
+  providers: [ChatService],
+  exports: [ChatService],
+})
+export class ChatModule {}