Integrate stricter linting for handwritten TS

Internally at Google we have a pretty strict TS style guide and linting. Our handwritten libraries should be held to the same standard, especially in regards to type safety as this will help us prevent breakages in the future.

This may involve multiple steps:
* Settle on a shared, repository wide set of linting standards and codify it into a shared ES Lint configuration.
* Add comments exempting all existing violations (especially in handwritten libraries).
* Burn down all of the exceptions until our libraries can pass the linter.