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/modules/early-access/early-access.service.ts

@@ -0,0 +1,42 @@
+import { Injectable, Logger } from '@nestjs/common';
+import { InjectRepository } from '@nestjs/typeorm';
+import { Repository } from 'typeorm';
+import { EarlyAccessSignup } from '../../entities/early-access-signup.entity';
+import { CreateEarlyAccessDto } from './dto/create-early-access.dto';
+
+@Injectable()
+export class EarlyAccessService {
+  private readonly logger = new Logger(EarlyAccessService.name);
+
+  constructor(
+    @InjectRepository(EarlyAccessSignup)
+    private readonly repo: Repository<EarlyAccessSignup>,
+  ) {}
+
+  async register(dto: CreateEarlyAccessDto): Promise<{ success: true; alreadyRegistered: boolean }> {
+    const existing = await this.repo.findOne({ where: { email: dto.email } });
+    if (existing) {
+      // Duplicate email — return friendly success rather than a 409 that would break the UX
+      return { success: true, alreadyRegistered: true };
+    }
+
+    const signup = this.repo.create({
+      email: dto.email,
+      server_count: dto.server_count ?? 'not specified',
+    });
+
+    try {
+      await this.repo.save(signup);
+    } catch (err: unknown) {
+      // Guard against a race-condition duplicate (unique constraint violation)
+      const pg = err as { code?: string };
+      if (pg.code === '23505') {
+        return { success: true, alreadyRegistered: true };
+      }
+      this.logger.error('Failed to save early-access signup', err);
+      throw err;
+    }
+
+    return { success: true, alreadyRegistered: false };
+  }
+}