Use API-Extractor to document the public API

[orta]

This PR microsoft/rushstack#1537 might be the last blocker on getting the typescript compiler API working on the site

[octref]

Seems resolved and look forward to the API 😉

[typescript-bot]

Hello! As per #2804, we are automatically closing all open issues. Please see #2804 for a description of what issues and PRs can be accepted going forward.