🚀 Feature: Switch eslint.config.js to eslint.config.ts

### Feature Request Checklist

- [x] I have pulled the latest `main` branch of the repository.
- [x] I have [searched for related issues](https://github.com/JoshuaKGoldberg/create-typescript-app/issues?q=is%3Aissue) and found none that matched my issue.

### Overview

Now that Node.js has stable type stripping without a warning (https://github.com/nodejs/node/pull/58643) and ESLint supports it natively (https://github.com/eslint/eslint/issues/19357), we should be able to switch the ESLint config from `.js` to `.ts`. That'd be the last JS config file added to `--preset everything` switched to TS.

### Additional Info

Blocked on the warning-less type stripping being released in the next minor version of Node.js.

Inspired by @michaelfaith's https://github.com/JoshuaKGoldberg/eslint-plugin-package-json/pull/1112.

🎁