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webpack-dev-server not building / compiling

The webpack-dev-server serves the result from memory. It doesn't write to file system or disk.
When you start webpack-dev-server from CLI it says
webpack result is served from /
indicates that your bundle is served from /. You need to tell the webpack-dev-server where your assets should be served by setting publicPath. If you have public/index.html
// index.html
<!DOCTYPE html>
    <head> ... </head>
        <div id="app"></div>
        <script src="/assets/js/app.js"></script>

And your bundled javascript is served from 'public/assets/js' then you need to tell webpack to serve the assets from '/assets/js' by setting publicPath property.
output: {
    path: path.join( __dirname, 'public/assets/js'),
    publicPath: 'assets/js/',
    filename: 'app.js'