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/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"