What problem does this feature solve?

It adds autocompletion in eslintrc and allows type-checking it.

What does the proposed API look like?

This can be done by installing @types/eslint and then adding the following type declaration to the top of the generated .eslintrc.js file:

/**
 * @type {import('eslint').Linter.Config<import('eslint/rules/index').ESLintRules>}
 */

This might be possible to instead do in a separate .d.ts file, but I'm not very proficient in typescript yet.

I'm not sure how to configure the type-checking to actually run on .eslintrc.js.