webpack not generating css file

webpack does not create separate css files. It get's bundled with the javascript and is injected into the DOM as style tags by webpack bootstrap code.

If you want to create separate css file, you can use the ExtractTextPlugin - https://github.com/webpack-contrib/extract-text-webpack-plugin

const ExtractTextPlugin = require("extract-text-webpack-plugin");

module.exports = {
  module: {
    rules: [
      {
        test: /\.css$/,
        use: ExtractTextPlugin.extract({
          fallback: "style-loader",
          use: "css-loader"
        })
      }
    ]
  },
  plugins: [
    new ExtractTextPlugin("styles.css"),
  ]
}

ExtractTextPlugin is deprecated try https://github.com/webpack-contrib/mini-css-extract-plugin:

const MiniCssExtractPlugin = require('mini-css-extract-plugin');
module.exports = {
  plugins: [
    new MiniCssExtractPlugin({
      // Options similar to the same options in webpackOptions.output
      // all options are optional
      filename: '[name].css',
      chunkFilename: '[id].css',
      ignoreOrder: false, // Enable to remove warnings about conflicting order
    }),
  ],
  module: {
    rules: [
      {
        test: /\.css$/,
        use: [
          {
            loader: MiniCssExtractPlugin.loader,
            options: {
              // you can specify a publicPath here
              // by default it uses publicPath in webpackOptions.output
              publicPath: '../',
              hmr: process.env.NODE_ENV === 'development',
            },
          },
          'css-loader',
        ],
      },
    ],
  },
};