feat(api): early-access signup endpoint (POST /api/early-access)

Real @Public() NestJS endpoint persisting to the existing early_access_signups table (email + server_count), matching the schema exactly (no migration). Duplicate-email safe (pre-check + unique-constraint catch -> friendly success). Wired into app.module. Makes the marketing early-access form functional end-to-end on next API deploy. tsc/nest build green.

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

backend-nest/src/app.module.ts

@@ -44,6 +44,7 @@ import { FurnaceSplitterModule } from './modules/furnacesplitter/furnacesplitter
 import { BetterChatModule } from './modules/betterchat/betterchat.module';
 import { TimedExecuteModule } from './modules/timedexecute/timedexecute.module';
 import { RaidableBasesModule } from './modules/raidablebases/raidablebases.module';
+import { EarlyAccessModule } from './modules/early-access/early-access.module';
 
 // Shared Services
 import { NatsService } from './services/nats.service';
@@ -123,6 +124,7 @@ import { NatsBridgeGateway } from './gateways/nats-bridge.gateway';
     BetterChatModule,
     TimedExecuteModule,
     RaidableBasesModule,
+    EarlyAccessModule,
   ],
   providers: [
     // Global guards (order matters: auth first, then license, then permissions)