Set Up Database Module with TypeORM and Migrations

[Mkalbani]

Description

Configure a database module that bootstraps TypeORM with PostgreSQL, registers all entities, and integrates database migrations into the development and deployment workflow. A solid database setup from the start prevents painful schema drift and ensures the team can evolve the data model confidently as new modules are added.

Acceptance Criteria

• A database module is scaffolded at src/database/
• TypeORM is connected to PostgreSQL using env-based config
• All entities are auto-discovered and registered via TypeOrmModule.forFeature
• Migrations are configured and a first migration generates the initial schema
• npm run migration:generate, migration:run, and migration:revert scripts are available
• synchronize is set to false in all non-local environments
• Connection failure at startup logs a clear error and exits the process
• A seed script populates dev/test databases with sample puzzles and users