According to caniuse, Opera supports the Speech Recognition API. However, when attempting to view a simple example, I cannot find the “allow” button alluded to upon click of the microphone icon. In Chrome, the allow microphone dialog immediately pops up when the microphone icon is first clicked.
I’m testing on a clean install of Opera 39/Mac.
Like HiDeo said, according to https://developer.mozilla.org/en-US/docs/Web/API/SpeechRecognition#Browser_compatibility they do not support webkitSpeechRecognition.
But the real issue here is that you are not getting prompted to allow the use of your mic. Double check this is correct.
To always allow sites access to your camera and microphone:
Ultimately, even if you get the mic issue working, you won’t be able to use the speechRecognition anyways. If you really want to support Opera (and other browsers), you should think about using IBM bluemix, or Google’s new speech to text (in Beta).