I'm curious how Webrender is able to render native controls (buttons, text inputs, etc.) via this method - I suppose they have access to APIs not exposed in e.g. WebGL that make this trivial?
Not really, unfortunately. Native toolkits aren't designed for this. As an example, I looked into using HIToolbox (the API Apple uses) for this on the Mac, but it was so obviously unsupported and likely to break at any time that I quickly decided against it.