Make Schema a discriminated union (#296)

* Make Schema a discriminated union

This leverages the type system to better describe the API's requirements for schemas. For example, rather than saying that any schema might have an optional `items` property, we're able to express that `items` is required on array schemas and forbidden on all others.

More info on discriminated unions: https://www.typescriptlang.org/docs/handbook/2/narrowing.html#discriminated-unions

* Update docs.

Fix requestOptions in startChat (#228)