Add some CI checks for TypeScript type definitions

[luser]

Our TypeScript type definitions in this repository are hand-authored and because the SDK itself is not written in TypeScript it's possible for us to ship things that tsc won't accept. #144 is an example of one such thing. I asked for more details from the author of that PR, because I suspect that there's also a TypeScript version / configuration angle to this.

We should have some checks in this repo's CI to validate the TS types, ideally against a matrix of TS versions. If configuration matters, then doing so in the most-strict configuration possible would be ideal.