telemetry_json: Use the PImpl idiom to avoid unnecessary dependency exposure

Users of the web_service library shouldn't need to care about an
external library like json.h. However, given it's exposed in our
interface, this requires that other libraries publicly link in the JSON
library. We can do better.

By using the PImpl idiom, we can hide this dependency in the cpp file
and remove the need to link that library in altogether.