Upgrading to babel-eslint@11

Hi! First of all, thanks for AST Explorer. As a maintainer of ESLint, this tool has been invaluable to my work ❤️

I've been doing some work on babel-eslint, and as of [the latest release](https://github.com/babel/babel-eslint/releases/tag/v11.0.0-beta.0), babel-eslint will now start reading your Babel config file at parse time.

I haven't had time to look into how AST Explorer is set up yet, but I'll try to find some time to figure out a strategy for how we can get this to work. Wanted to make an issue so we can have a place to discuss.

The issue names no files, tests, or entry points. Start by locating AST Explorer's babel-eslint dependency and how Babel configuration is handled during parsing, then verify that babel-eslint@11.0.0-beta.0 can parse the supported examples without breaking existing behavior.

Written by the indexing model from the issue text.