I'm not sure. I'm not into chess but I've watched other strategy games; I'm fairly confident streamers are vocalizing a lot more than they would actually be consciously considering if they weren't streaming.

Back in the day I remember Jon Finkel (a legendary Magic: the Gathering pro) saying* you're supposed to "focus only on what matters."

It stuck with me because I think it's genuinely what they do, but also seems like completely useless advice. I don't know what matters! That's what makes you a pro and me not.

* Wasn't sure if my memory was correct. A web search finds a Mike Flores article citing Zvi calling this Finkel's Law.