I have experimented some time ago on this topic, by choosing a small pool of plausible products, verifying they were not appearing in my ads, and then discussing far and wide a randomly-chosen half of them with trusted friends involved in the same experiment, and carefully not discussing the others.

After some time we also searched for half of them on the Internet and checked the results.

You can run your own tests on this matter, adopting the same protocol. This should help you clear how the matter lies.

My own conclusions so far (TL;DR there is nothing afoot):

The obvious

If you use a search term with Siri or Alexa or whatever, then the search term ends up in Google Ads, Amazon and so on, not at the same speed.

Once you explicitly search for something on the Internet, all bets are off, and the various advertising-enabling companies will share your data with all advertisers (so expect to buy something on Amazon and find it on Facebook, even if it's annoying like hell - I have already bought the thing, for crying out loud!).

The less obvious

This seems to happen (but we have no hard data for a confidence evaluation) even if you are not actively searching for the term, and the Internet-connected listening appliance is just sitting nearby, listening for the activation phrase.

This stands somewhat to reason. The appliance is "thinking": "Is 'Honey' 'Hey Google'? No." "Is ', how about' 'Hey Google'? No." "Is 'a nice cup of Earl Grey' 'Hey Google'? No." -- but to do this, it might well happen that "Earl Grey" makes its way into the corporate servers for tuning and verification of voice recognition, and some other corporate app might sometimes troll the database for leads.

(Normally, unless the utterance matches the activation cue, the sound bite is not transmitted to the corporate servers. It can be in case of "accidental activations", as @Tim noted. But usually manufacturers reserve the right of downloading "selected sound bites" (for example, and I'm pulling this out of my left ear: whatever reaches 90% of the recognition threshold for "Hey, you!" without reaching the 99% required for device activation, say 'Kaiju'. This allows the manufacturer to tune the device so that it has a stronger rejection of words like 'Kaiju').

Also, "listening" and decoding information from unconventional sources or through unconventional means would incur enormous costs for very little advantage, and the very real risk of alienating one's customer base and/or incurring in lawsuits. It seems to me as if it wouldn't be worth the advertiser's while.

Finally, your "propensity" for a given item might depend on some complex demographic. For instance, you talk about buying a Foobaz with a friend of yours (living nearby etc.). Once you have bought your Foobaz, he is in a group of people where Foobaz sales have just gone up by exactly one piece. So his data are sold as "people who are more likely than average to buy a Foobaz".

From your friend's point of view, he talked with you about a Foobaz, and the next day bam!, he's offered one on Google Ads!

That's why in the test it is important to choose an article you never wanted, and never discuss it with anyone (also, beware of prankster friends :-) ).

The not always so obvious

Lots of new product are advertised to me every week. Usually I don't notice them except as a very low-level nuisance, as I'm not remotely thinking about them .

But by mere chance, some product might come by which is trending, and I saw somewhere else and I talked to someone about, or just happened to think about. When this ad comes by, I feel a jolt and notice it, and remember (it is a form of the "Baader-Meinhof effect").