TypeScript tooling, pt. 1

[thompsongl]

Summary

Starting a chip-away-at-it set of PRs to fully (finally) complete the migration from JS to TS, with an emphasis on build tooling.
Scope is not entirely clear right now, this is 1 of n.

In this one:

• Delete last .js files in src/
• Start the transition away from packages/ code in the bundle
• Resolve some types errors that arose from the move

Thinking about:

• Probably a breaking change to remove Packages from index.ts
• Perhaps a better way to handle react-datepicker (new index.d.ts in packages/)

Checklist

• Check against all themes for compatibility in both light and dark modes
• Checked in mobile
• Checked in Chrome, Safari, Edge, and Firefox
• Props have proper autodocs and playground toggles
• Added documentation
• Checked Code Sandbox works for the any docs examples
• Added or updated jest tests
• Checked for breaking changes and labeled appropriately
• Checked for accessibility including keyboard-only and screenreader modes
• A changelog entry exists and is marked appropriately

[kibanamachine]

Preview documentation changes for this PR: https://eui.elastic.co/pr_4695/

[thompsongl]

Closing in favor of a better scoped #5034. Feel free to re-open if this still works as a starting point.