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Chrome's Web Speech API does indeed send audio to Google's servers by default unless you're using the newer SpeechRecognition API with continuous=false and interimResults=true for local processing.
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It seems to send the data to google's servers.

> Note: On some browsers, like Chrome, using Speech Recognition on a web page involves a server-based recognition engine. Your audio is sent to a web service for recognition processing, so it won't work offline.

https://developer.mozilla.org/en-US/docs/Web/API/Web_Speech_...

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