Babel is a tool to convert ECMAScript 2015+ code into a backwards compatible version of JavaScript. It transform new syntax into old one, apply polyfills, and more.
In webpack use babel-loader to transpile ES2015+ code to support older browsers.
babel.config.js handle Babel configuration.
You'll need @babel/preset-env to be able to transpile your javascript code. It can be configured to include only transforms needed for the browsers you want to support. It can also be set to load the needed polyfills (see babel-polyfill example).
By setting browserslist you can choose which browser to target for your final bundle. In this example it's set inside package.json.
Read comments inside src/*js files. Run the build npm run dev and inspect results inside dist folder.
Tree shaking should works by default when running in production mode, if there are problems you can set babel modules option to false.
You may also want to use babel-plugin-transform-imports to load only specific part of an ES2015 library.
If you have problem with dynamic import try to add syntax-dynamic-import Babel plugin.