Configure ESlint with next

It looks like we could improve our eslint configuration with next: https://nextjs.org/docs/basic-features/eslint#migrating-existing-config

And we should investigate why we have a `.babelrc` and whether we should keep it and for what purpose.

Start with the Next.js ESLint migration guidance linked in the issue, then inspect the existing ESLint configuration and `.babelrc`. Configure the project according to the applicable Next.js guidance and determine whether `.babelrc` is still needed and why; done means both configuration questions have a clear resolution.

Written by the indexing model from the issue text.