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/jest.config.js

@@ -0,0 +1,16 @@
+/**
+ * Jest config for the UlHub backend (NestJS).
+ * ts-jest transpiles the TypeScript sources; decorators/metadata are honored via tsconfig.
+ * Specs live next to sources as *.spec.ts (unit) — e2e would go under test/ with a separate config.
+ */
+module.exports = {
+  moduleFileExtensions: ['js', 'json', 'ts'],
+  rootDir: 'src',
+  testRegex: '.*\\.spec\\.ts$',
+  transform: {
+    '^.+\\.ts$': ['ts-jest', { tsconfig: '<rootDir>/../tsconfig.json' }],
+  },
+  collectCoverageFrom: ['**/*.(t|j)s'],
+  coverageDirectory: '../coverage',
+  testEnvironment: 'node',
+};

backend/package.json

@@ -8,7 +8,9 @@
     "build": "nest build",
     "format": "prettier --write \"src/**/*.ts\"",
     "postinstall": "prisma generate",
-    "db:seed": "ts-node prisma/seed.ts"
+    "db:seed": "ts-node prisma/seed.ts",
+    "test": "jest",
+    "test:ci": "jest --ci --runInBand"
   },
   "prisma": {
     "seed": "ts-node prisma/seed.ts"
@@ -44,9 +46,12 @@
     "@types/cookie-parser": "^1.4.7",
     "@types/express": "^4.17.17",
     "@types/node": "^20.11.0",
+    "@types/jest": "^29.5.12",
     "@types/passport-jwt": "^4.0.1",
     "@types/ws": "^8.5.10",
+    "jest": "^29.7.0",
     "prettier": "^3.0.0",
+    "ts-jest": "^29.2.5",
     "prisma": "^6.10.0",
     "ts-node": "^10.9.1",
     "typescript": "^5.5.0"

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',
+    });
+  });
+});