In theory this should be easy to test I thought but in less than one minute after starting I realized it’s much easier to taint the research in trivial ways. In short I took a Samsung from a relative that had everything Google installed, including the assistant (although without the “OK Google” feature) and started to shout at it “fishing rods”. Next thing I know after leaving the phone idle for a while a take it, open the browser (Chrome!) but in the meantime absent mindendly I enter already fishing in the search bar which (without even tapping search) promptly gets completed with a couple suggestions (like fishing tackle, fishing club, fishing rods and so on!!!).
This should be a double (at least) blind test, with somebody shouting at the phone (preferably from some commercial products chosen at random) and then somebody else (maybe the device owner) reporting what he’d got.
Also this part is completely unproved (and should be easily provable by just building your own app that extracts anything from what people talk):: In the absence of these triggers, any data you provide is only processed within your own phone. This might not seem a cause for alarm, but any third party applications you have on your phone—like Facebook for example—still have access to this “non-triggered” data.