Introduce Typescript build process, generate types

Now that there is a manually written `index.js` as the entrypoint, we're duplicating a lot of work between `index.js` and `index.d.ts` that is error prone. Write an `index.ts` that replaces both in the repo, and a build process that produces both of the original files for NPM packaging.

Start with the existing index.js and index.d.ts entrypoint files, then determine how an index.ts can replace them while preserving the package interface. Define the build process around generating both original files for NPM packaging; done means the generated outputs match the package's required entrypoints.

Written by the indexing model from the issue text.