Given the power demands of such an always-on analysis engine, that would show in battery runtime. At least if it's happening while the device is not plugged in.
Maybe (just an hypothesis) there could be a set of other keywords also listened for, that once detected could start another more complex routine. Like that, you could limit the battery impact, and yet be able to listen to the users for advertising purpose.
Then again, I opened Instagram at a carwash once, and a few days later I got ads about car treatment products. I walked by an e-bike store the other day and stopped for about 15 seconds to look at the bikes being displayed, and a few days later Instagram started showing me ads for the brand. I thought Instagram or another Zuck-app was tracking my location, but I just checked and none of the Zuck-apps on my phone have location permission enabled.