Silly me imagined for some reason Phoenix had some flags for this.

Updated my webpack.config.js and now works as expected:

• added stats: 'minimal', (which “Only output when errors or new compilation happen”) to module.exports return object

• configured HardSourceWebpackPlugin info to level: 'warn' (which “reports warn and error level messages”)".

Final result

❯ mix phx.server
[info] Running HelloWeb.Endpoint with cowboy 2.8.0 at 0.0.0.0:4000 (http)
[info] Access HelloWeb.Endpoint at http://localhost:4000

webpack is watching the files…

webpack.config.js

❯ cat assets/webpack.config.js
const path = require('path');
const glob = require('glob');
const HardSourceWebpackPlugin = require('hard-source-webpack-plugin');
const MiniCssExtractPlugin = require('mini-css-extract-plugin');
const TerserPlugin = require('terser-webpack-plugin');
const OptimizeCSSAssetsPlugin = require('optimize-css-assets-webpack-plugin');
const CopyWebpackPlugin = require('copy-webpack-plugin');

module.exports = (env, options) => {

  const devMode = options.mode !== 'production';

  return {
    stats: 'minimal',  #<-------Add kv------->
    optimization: {
      minimizer: [
        new TerserPlugin({ cache: true, parallel: true, sourceMap: devMode }),
        new OptimizeCSSAssetsPlugin({})
      ]
    },
    entry: {
      'app': glob.sync('./vendor/**/*.js').concat(['./js/app.js'])
    },
    output: {
      filename: '[name].js',
      path: path.resolve(__dirname, '../priv/static/js'),
      publicPath: '/js/'
    },
    devtool: devMode ? 'eval-cheap-module-source-map' : undefined,
    module: {
      rules: [
        {
          test: /\.js$/,
          exclude: /node_modules/,
          use: {
            loader: 'babel-loader'
          }
        },
        {
          test: /\.[s]?css$/,
          use: [
            MiniCssExtractPlugin.loader,
            'css-loader',
            'sass-loader',
          ],
        }
      ]
    },
    plugins: [
      new MiniCssExtractPlugin({ filename: '../css/app.css' }),
      new CopyWebpackPlugin([{ from: 'static/', to: '../' }])
    ]
    .concat(devMode ? [new HardSourceWebpackPlugin({
      #<-------Add obj------->
      info: {
        level: 'warn'
      }  
    })] : [])
  }
};