The packages that you have shown above are all development dependencies so you need those only on your machine in order to perform development. When you build it later on using
npm run dev or
npm run prod, it will get transformed into JS code.
So if you say that it the app works on your production server where you want to deploy the app that means that you have the packages that you use globally accessible on the server, or otherwise it will not work 100%.
So you don't need to run
npm install because that will install all the
dependencies along with the
devDependencies, so you should use
npm install --only=prod (or
--only=production) to install only
dependencies, and not
devDependencies, regardless of the value of the NODE_ENV environment variable.
Note: if you don't have
dependencies in your package.json, then there is no need to do this on production server.