[M1] Establish NestJS API testing baseline

[rodrigolinhas]

Goal

Ensure V2 begins with automated tests instead of carrying V1's zero-test baseline forward.

Expected Scope

• Unit tests only where they add value.
• Integration/API tests using Supertest or appropriate equivalent.
• Isolated test configuration (.env.test).
• Database-test strategy.
• Deterministic test setup/cleanup.

Acceptance Criteria

• V2 has a working automated test command (npm run test:v2 or similar).
• At least one Nest application/API test executes successfully.
• Health/readiness behavior is tested.
• Test database state is deterministic.
• Tests do not destroy developer V1 SQLite data.
• Tests do not depend on manually created local state.

Dependencies

• Issue A ([M1] Bootstrap NestJS V2 backend #6): [M1] Bootstrap NestJS V2 backend.
• Database integration tests depend on Issue B ([M1] Add PostgreSQL development environment #7) and Issue C ([M1] Configure PostgreSQL persistence and versioned migrations #8).

Suggested PR

PR 3 — Health/readiness + OpenAPI + testing foundation (with Issues E and F)