In debugging  issue #801237 , I noticed the extension wasn't being consulted after HTTP auth was requested. The state machine diagram here says the request/response flow repeats after onAuthRequested:
https://developer.chrome.com/extensions/webRequest

However, the ClearSignaled / GetAndSetSignaled logic in ExtensionWebRequestEventRouter does not reflect this. As a result, extensions do not see the subsequent HTTP request/response.