[email protected] requires a peer of webpack@^4.x.x but none is installed

webpack-dev-server has Webpack as a peer dependency, which means that you are responsible for installing that yourself.

You could install the latest version of Webpack and add it to your devDependencies with the following command:

npm i -D webpack@latest

By writing webpack-dev-server you are also trying to use the globally installed version of that package. You can use the locally installed one instead by adding it to a script in your package.json:

{
  "scripts" : {
    "start": "webpack-dev-server"
  }      
}