5-VED/NestJs ? reverse-engineered prompt

Build me a clean NestJS starter app in TypeScript that I can use as a boilerplate for future backend projects.

I want the usual setup to be ready to run, with a simple app that starts in development mode, production mode, and watch mode, plus unit tests and end to end tests already wired up. Please include sensible linting and formatting defaults, a sample environment file, and a basic project structure that follows NestJS best practices so it’s easy to add new features later.

Keep it minimal but polished, with a working hello world style endpoint or starter controller so I can verify everything is set up correctly. Make sure the app runs without extra manual steps after install, and leave clear scripts in place for starting the app and running tests. If you need to check current NestJS docs for any setup details, feel free to do that.