I have been down in the weeds with both Amazon's and Google's engineers on how their products work. We've monitored them in the lab to verify claims, as best we can. The machine in your shop or living room is essentially continuously recording in the digital equivalent of a short loop of tape. Recognition of the trigger word is local. Once recognized, the machine sends about 5 seconds of recording from pre-trigger through some variable length of time after to Amazon or Google (I assume Apple works the same way, but have no experience with them). On the consumer versions of the products, a lot of that is stored. In the medical versions, they "forget" it rather quickly, in an attempt to remain HIPAA privacy rule compliant.
So, no, the soundscape of your room is not being continuously transmitted to these vendors. But they do reserve the right to store and reprocess what is sent into the cloud. Whether that bothers you or not is up to you. Obviously Jim has concluded it's unimportant. I've reached the opposite conclusion, so use mine only in the shop, where the only voice it's going to hear is mine, and that very rarely, unless I'm asking it to start or stop an audiobook. Occasionally, I'LL ask it for the time. I don't talk to myself much. On the other hand, my first generation echo had an ongoing relationship with a couple of my shop tools for some years. Tool sounds would sometimes do wake "computer" (I refuse to address a machine with a human name) up. "I'm sorry, I didn't get that" was a pretty common refrain in the shop for a while. It's pretty much stopped though, as the software in the device has been continuously improved.