I haven't seen any credible evidence that any of the reputable brands of smart speakers send anything other than what you want to send (e.g. the sentence after you say the watchword) to their servers.

Yes they are constantly listening, but this is just for the watch word (as a cue to start listening/sending) but they lack the on-device ability to convert anything else to text on their own. All they can do on their own is listen out for the watch word.

Certain smart TVs on the other hand, are known to constantly stream audio back to their HQ as they don't have on-board watchword detection.