Test the product catalogue feature (UC-010)

Problem Description

An online shop's NestJS + Drizzle backend has a fully implemented products feature at apps/api/src/products/ — module, controller, service, repository, and DTOs. It serves GET /api/products with an optional category query parameter, and it has no tests at all.

The use case it implements is specified at docs/use_cases/UC-010-browse-product-catalog.md, including alternative flow A1 and business rule BR-010.

The project has Vitest configured for unit tests (vitest.config.ts, npm run test:unit) and a test:e2e script, but no end-to-end test has ever actually been written or run — there is no e2e test directory and no test infrastructure beyond the unit config. The application boots against PostgreSQL and its global ValidationPipe is configured with whitelist, forbidNonWhitelisted, and transform.

Output Specification

Write tests for UC-010 at both levels:

1. Unit — cover the service's logic and its mapping to the response shape, without a database.
2. End-to-end — cover the endpoint's real behaviour over HTTP, including the main success scenario, alternative flow A1, and business rule BR-010, against a real PostgreSQL database rather than a substitute.

Make whatever configuration changes the tests need in order to run.