"look into" is a much more likely trigger, then send the 30 seconds before and after to a server for more analysis. "buying" could be another. It's not like it would be that hard. Especially with some of the pretty good vocal compression for audio. It would be a small blip on a modern connection, even wireless.

I'm not saying it is or isn't happening but it wouldn't be hard.

Your argument plays with the idea that the phone listening stuff is the only source of information for the ad networks. But it would be much more complex. It would be only one of many signals, that are used to serve the consumer the right advertisement in the right moment. So it doesn't need to have the exact phrase "pool fencing" in the database. It just need to detect that something about pools, or swimming, etc. was talked about. Since Google has thousands of signals and statistics (like browsing history, current location, the other smartphones that are near, and those histories etc.) about this person, it can sell the ad space to "pool fencing" and expect a high click through rate. Selling ads is a bit like the current LLMs. It's just a stochastic parrot, that hallucinates stuff. But the stuff is often that advertisement that brings in the most money.

I dont know if phones listen to us to serve ads, but 11K is a decent vocab. Most adults have a vocab of 20K. Therefore I could imagine it including the words "pool" and "fencing".