I have been unable to get the Google Demo for the WebkitSpeechRegognizer working under QWebEngineView. The page never emits the featurePermissionRequested signal and manually setting feature permissions for QWebEnginePage::Feature::MediaAudioVideoCapture and QWebEnginePage::Feature::MediaAudioCapture made no difference on the issue.

I have tried using the command line option --use-fake-ui-for-media-stream and I found an article on Chromium Issues where the flag doesn't fix the permission, I have a suspicion that there is a separate permission required for voice recognition perhaps. Chromium Thread

Google Webkit Speech Demo