How to resolve webpack-stream module not found errors with webpack 5?

I'm trying to use the node puppeteer library in a Chrome extension. I'm using the extension-cli build tool, which uses webpack under the hood, but when I try to build I get errors regarding multiple missing modules such as:

Error in plugin "webpack-stream"
Message:
Module not found: Error: Can't resolve 'fs' in '/path/to/my/project/node_modules/chownr'
Module not found: Error: Can't resolve 'path' in '/path/to/my/project/node_modules/chownr'

BREAKING CHANGE: webpack < 5 used to include polyfills for node.js core modules by default.
This is no longer the case. Verify if you need this module and configure a polyfill for it.

If you want to include a polyfill, you need to:
    - add a fallback 'resolve.fallback: { "path": require.resolve("path-browserify") }'
    - install 'path-browserify'
If you don't want to include a polyfill, you can use an empty module like this:
    resolve.fallback: { "path": false }

I understand the reason for the errors and I have installed all 11 related core node packages that are affected. I've also created the following webpack.config.js file in my project root directory (alongside the node_modules dir) with the following:

module.exports = {
  resolve: {
    fallback: {
      "path": require.resolve("path-browserify"),
      "assert": require.resolve("assert/"),
      "constants": require.resolve("constants-browserify"),
      "crypto": require.resolve("crypto-browserify"),
      "http": require.resolve("stream-http"),
      "https": require.resolve("https-browserify"),
      "os": require.resolve("os-browserify/browser"),
      "stream": require.resolve("stream-browserify"),
      "url": require.resolve("url/"),
      "util": require.resolve("util/"),
      "zlib": require.resolve("browserify-zlib"),
    }
  }
}

I'm still getting the exact same errors during the build though. Do I have to put the config above somewhere else?