[Docs Site] support parsing inherited/imported/extended types

[brian-smith-tcril]

Came up in #4221 (comment)

Something like TypeDoc would have a much better "understanding" of the TypeScript types, but be missing most other features we expect on the docs site.

I figure we can work with what we have for now with the current docs site, but we should try to do it better if we're making a new one.