Imo the truth is much scarier: advertises know us better than we known ourselves. There's also the idea that we are so alike, advertises can generalize to great success.
I think you mean confirmation bias. Observer bias is similar, but relates to being non-blinded during a scientific study.
Baader-Meinhof phenomenon or Frequency illusion could be what we were seeking?
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.