Replace deprecated eslint-loader with eslint-webpack-plugin

[aaemnnosttv]

Bug Description

The eslint-loader package is now deprecated and eslint-webpack-plugin is recommended in its place.

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Acceptance criteria

• The functionality provided by eslint-loader should be replaced with eslint-webpack-plugin
  See https://github.com/webpack-contrib/eslint-webpack-plugin#migrate-from-eslint-loader

Implementation Brief

• Install eslint-webpack-plugin as a development dependency;
• Delete eslint-loader dependency;
• Remove eslint-loader from the common rules array: https://github.com/google/site-kit-wp/blob/026f7d3e022356335c420d276fdd31366ea6342c/webpack.config.js#L117-L123
• Create a new plugins array similar to the rules one and add the ESLintPlugin plugin to it;
  • Pass options from the eslint-loader to the eslint plugin constructor.
• Destruct plugins array in the plugin section of each configuration as we do it with the rules array.

Test Coverage

• Not needed

Visual Regression Changes

• No visual changes are expected

QA Brief

• Make sure the eslint plugin catches formatting errors when you build assets.

Changelog entry

• N/A

[aaemnnosttv]

IB ✅

[Hazlitte]

QA ✅ I tested npm builds and watch and edited a few different files with linting errors. All errors were caught.