Add TypeScript type-checking to all rules

[bmish]

We don't need to convert our JavaScript files to TypeScript, but by adding JSDoc comments with types and using the TypeScript checkJs option, we can get the benefits of type-checking. See this PR for an example and list of benefits: square/eslint-plugin-square#723.

[platinumazure]

I'm on board in principle, but I would want to make sure the developer burden is not significantly increased.

I skimmed the PR but need to look through it more thoroughly.

[platinumazure]

@bmish Finally coming back to this... I'm open to this but I have one question. How do we ensure that type info (in doc comments) is added for new code/types? And are there ways to auto-generate at least some of those so the dev experience isn't too annoying?