test: wire jest harness for QA gate (S1-f)

Add jest + ts-jest to the NestJS backend with an app.service smoke spec that
exercises Nest DI. `npm test` is the documented command the QA gate runs.

Trace: SRS §6 gate, NFR-8.

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

backend/src/app.service.spec.ts

@@ -0,0 +1,27 @@
+import { Test, TestingModule } from '@nestjs/testing';
+import { AppService } from './app.service';
+
+// Smoke test for the QA gate (S1-f, trace: SRS §6 gate / NFR-8).
+// Exercises Nest DI wiring end-to-end for a pure service so a green run proves the
+// toolchain (ts-jest + @nestjs/testing) is functional. Real coverage grows from here.
+describe('AppService (smoke)', () => {
+  let service: AppService;
+
+  beforeEach(async () => {
+    const moduleRef: TestingModule = await Test.createTestingModule({
+      providers: [AppService],
+    }).compile();
+    service = moduleRef.get<AppService>(AppService);
+  });
+
+  it('is resolvable from the DI container', () => {
+    expect(service).toBeDefined();
+  });
+
+  it('returns the API welcome payload', () => {
+    expect(service.getHello()).toEqual({
+      message: 'Welcome to UlHub API',
+      docs: 'GET /api',
+    });
+  });
+});