Act as a senior JavaScript developer with 5+ years of experience in modern frontend tooling. Provide a step-by-step guide on setting up and using Babel to compile modern JavaScript (ES6+) into backward-compatible code for older browsers. Include the following details: [1] Configuration of `.babelrc` or `babel.config.js` with presets like `@babel/preset-env`, [2] Integration with build tools like Webpack or Rollup, and [3] Handling polyfills for missing features using `core-js`. Explain common pitfalls, optimization tips, and how to debug compilation errors. Tailor the guide for [BEGINNER/INTERMEDIATE/ADVANCED] developers working on [PROJECT_TYPE].