Add support for the -f flag for linting styles

[Veldrovive]

Describe the feature you'd like to request

We use the -f flag to support a testing suite that uses the checkstyle format. Standard eslint supports this through the -f checkstyle flag which the current next lint command does not support.

Describe the solution you'd like

Add support for the -f flag in the javascript api for eslint.
This PR adds a similar feature.

Describe alternatives you've considered

You can also run eslint directly, but it is unfortunate to have to use a different command for testing in the CI than in dev as there may be unforeseen differences.

[housseindjirdeh]

PR to land this here: #27052