Clean up DevOps playground configuration

[theShihamAhamed]

Summary

This PR cleans up and stabilizes the project after renaming it to DevOps Playground API.

The main goal of this change is to align the project naming, Docker configuration, environment setup, and development/production workflows with the new devops-playground direction.

Changes Made

• Renamed remaining project references to use devops-playground / devops-playground-api.
• Updated Docker image/container naming for development and production.
• Added explicit Docker image names for Compose builds.
• Renamed the misspelled auth route file from auht.routes.js to auth.routes.js.
• Updated the auth route import path.
• Updated logger service metadata to use the new API name.
• Updated GitHub Actions workflow metadata and Docker image naming.
• Updated test database fallback naming.
• Improved production script wording to reference the production app container and Neon Cloud correctly.
• Adjusted development Docker startup flow for Neon Local usage.
• Verified old naming references are removed from source/config files.
• Verified production Docker signup flow works.
• Verified development Docker signup flow works with Neon Local.

Testing

Manually tested using Docker and Postman:

• Production Docker build starts successfully.
• Development Docker build starts successfully.
• GET /health works.
• POST /api/auth/sign-up works in production Docker.
• POST /api/auth/sign-up works in development Docker.
• Verified Docker image name is now devops-playground-api.
• Verified the old project name is no longer present in real project source/config files.

Notes

• Real environment files are not intended to be committed.
• Production uses Neon Cloud directly.
• Development keeps Neon Local for local development workflow.
• Kubernetes support is planned for a later stage.