Earlier quoted context omitted.
I think it's the last option. His phone probably heard him ordering Voltaren. It's also the simplest possibility (Ockham's razor). I know because after discussing extremely rare chemicals at an officemate's desk, he began seeing ads for them. Neither of us had ever Googled or emailed anything related. It was a brand new idea for a brand new project which we had started working on that morning.
This is not the simplest possibility. Based on how often Google Home misunderstands the simplest queries, the tech is nowhere close to getting purchase intents out of random conversations. Besides that - do folks on hn really believe the „our phones are listening 24/7“ conspiracy theories?
My android phone often asks how did I like this or that shop. Sometimes I was just passing by those shops but on average the phone is quite correct which shops I have visited.
Google knows when you are in the pharmacy and might use a different routine interpreting ambient sounds when you are there. Voltarol (ibuprofen gel) is a distinct sound that even very lossy algorithm with low level of processing power can distinguish with a sufficient level of accuracy.