feat(03-02): add domaincheck backend - DNS service, API endpoint, module seed

- CheckDomainDto with regex validation (T-03-05) and max 10 TLDs (T-03-06)
- DomaincheckService using node:dns/promises with 5s timeout per lookup
- POST /modules/domaincheck/check protected by UseModule guard (T-03-08)
- DomaincheckModule seeds itself into registry on startup via OnModuleInit
- Default TLDs: de, com, net, org (D-03)

apps/api/src/domaincheck/domaincheck.controller.ts

@@ -0,0 +1,38 @@
+import { Body, Controller, Post } from '@nestjs/common';
+import { UseModule } from '../module-registry/module.guard';
+import { CheckDomainDto } from './dto/check-domain.dto';
+import { DomaincheckService } from './domaincheck.service';
+
+/**
+ * Controller for the Domaincheck module.
+ *
+ * POST /modules/domaincheck/check — accepts a domain label, checks TLD
+ * variants via DNS, and returns availability status for each.
+ *
+ * Protected by @UseModule('domaincheck') which ensures the requesting
+ * tenant has the domaincheck module activated (per T-03-08).
+ */
+@Controller('modules/domaincheck')
+@UseModule('domaincheck')
+export class DomaincheckController {
+  constructor(private readonly domaincheckService: DomaincheckService) {}
+
+  /**
+   * Check domain availability across TLD variants.
+   *
+   * @param dto - Contains domain label and optional TLD list
+   * @returns Domain and results array with tld, fqdn, and status
+   */
+  @Post('check')
+  async checkDomain(@Body() dto: CheckDomainDto) {
+    const results = await this.domaincheckService.checkDomain(
+      dto.domain,
+      dto.tlds,
+    );
+
+    return {
+      domain: dto.domain,
+      results,
+    };
+  }
+}