Just tried this on a vanilla Phoenix install.

/* This file is for your main application css. */
@import "./phoenix.css";
body {
  background-image: url("/images/phoenix.png");
  background-position: bottom;
  background-repeat: no-repeat;
}

works without any change to the stock webpack config:

const path = require('path');
const glob = require('glob');
const MiniCssExtractPlugin = require('mini-css-extract-plugin');
const UglifyJsPlugin = require('uglifyjs-webpack-plugin');
const OptimizeCSSAssetsPlugin = require('optimize-css-assets-webpack-plugin');
const CopyWebpackPlugin = require('copy-webpack-plugin');

module.exports = (env, options) => ({
  optimization: {
    minimizer: [
      new UglifyJsPlugin({ cache: true, parallel: true, sourceMap: false }),
      new OptimizeCSSAssetsPlugin({})
    ]
  },
  entry: {
      './js/app.js': ['./js/app.js'].concat(glob.sync('./vendor/**/*.js'))
  },
  output: {
    filename: 'app.js',
    path: path.resolve(__dirname, '../priv/static/js')
  },
  module: {
    rules: [
      {
        test: /\.js$/,
        exclude: /node_modules/,
        use: {
          loader: 'babel-loader'
        }
      },
      {
        test: /\.css$/,
        use: [MiniCssExtractPlugin.loader, 'css-loader']
      }
    ]
  },
  plugins: [
    new MiniCssExtractPlugin({ filename: '../css/app.css' }),
    new CopyWebpackPlugin([{ from: 'static/', to: '../' }])
  ]
});

So as suggested before - hand-type the image path into the app.css and see what happens.

package.json

{
  "repository": {},
  "license": "MIT",
  "scripts": {
    "deploy": "webpack --mode production",
    "watch": "webpack --mode development --watch"
  },
  "dependencies": {
    "phoenix": "file:../deps/phoenix",
    "phoenix_html": "file:../deps/phoenix_html"
  },
  "devDependencies": {
    "@babel/core": "^7.0.0",
    "@babel/preset-env": "^7.0.0",
    "babel-loader": "^8.0.0",
    "copy-webpack-plugin": "^4.5.0",
    "css-loader": "^2.1.1",
    "mini-css-extract-plugin": "^0.4.0",
    "optimize-css-assets-webpack-plugin": "^4.0.0",
    "uglifyjs-webpack-plugin": "^1.2.4",
    "webpack": "4.4.0",
    "webpack-cli": "^2.0.10"
  }
}

Hi,

body {
  background-image: url('/images/my-image.png');
}

<%= %> tags only works inside eex templates.

file-loader is the default fallback loader when the file exceeds the specified limit.

• install file-loader so that the fallback works
• increase the specified limit to be large enough so that your image will get processed (or remove it altogether).