Add OpenAPI documentation

### Description
Integrate Swagger/OpenAPI documentation into the project to provide clear and interactive API documentation for developers.

Read docs: https://docs.nestjs.com/openapi/introduction

### Tasks
- [ ] Install Swagger dependencies in the project.
- [ ] Configure Swagger for the Next.js project.
- [ ] Ensure the documentation is accessible via a specific route.
- [ ] Document the OpenAPI access route in the **README** file.

### Acceptance Criteria
- Swagger/OpenAPI documentation should be available and accessible.
- All existing API endpoints should be documented clearly.

Read the linked NestJS OpenAPI guide, then inspect the project's existing API endpoints and README to determine the integration points and documentation route. Done means Swagger/OpenAPI is accessible at a documented route, all existing endpoints are documented, and the README explains how to access it.

Written by the indexing model from the issue text.