I've been waiting for a WebspeechAPI implementation in Firefox for many years now but the only reason why I don't think it's happening is because maybe Mozilla lacks the funds to train the models for speech-to-text/text-to-speech, etc.
This gap will grow more and more as new machine learning features are introduced (e.g. natural lang page searching, better translation, etc) which would be very easy for Google to add to it's browser but very expensive for open source projects.