Upgrade the eslint dependency. Change the documentation and tests to use
the new configuration format. Also, upgrade Node.js in the build pipeline.

> When ESLint v10.0.0 is released (end of 2024 or early 2025 in all likelihood),
  the eslintrc configuration system will be completely removed.

https://eslint.org/blog/2023/10/flat-config-rollout-plans/#eslintrc-removed-in-eslint-v10.0.0

* Describe and test the usage only with flatconfig. It'll be the only config
  format soon. Who needs to retain `.eslintrc` can stay with eslint 8.
* ESLint 9 supports only Node.js `^18.18.0 || ^20.9.0 || >=21.1.0`.
* The formatter `eslint-tap` works, but because it doesn't follow the NPM
  package naming convention `eslint-formatter-*`, it has to be specified
  using a path to the script with the main exports.