Creates NestJS backend tests with Vitest — unit specs with stubbed repositories, and Supertest end-to-end specs that boot the application against a real PostgreSQL database in Testcontainers. Use when the user asks to "write backend tests", "test the API", "write an e2e test", "test the endpoint", or mentions Supertest, Testcontainers, NestJS testing, or Vitest for a NestJS project.