Today I was watching a few YouTube videos about groundwork with horses. First time I did that. Yes, I was logged in.
Later today, I hopped on Amazon to track one of my packages. And in my suggestions, there were horse grooming kits, halters and the like, even though I had never before looked for things like these on there.
My mail addresses are different on the two places, and so are, of course, my passwords. I am on Linux with Firefox, uBlock etc. So this must be an incredible coincidence, a miracle, mind-reading, or maybe witchcraft?
I wonder what I could tweak to make things like this happen less in future. I am thinking of adding a Pi-hole to my router, yet I am no longer so sure, if it would help?
I can see the devices you use mattering. Where were you watching the videos? Do you have the Amazon app installed on the same device, or on a device with a microphone? My tin-foil hat theory is that the Amazon app is always listening from your phone, based on similar things happening to my wife.
Something on stock Android phones is always listening though. I had a similar experience as OP where I had an IRL conversation once with my son about a product I don't normally talk about. My phone was unused & "asleep" nearby. An hour later at work I was inundated with ads for said product all over the internet in my Chrome browser on my work computer. It was way too heavy handed to be a coincidence. The phone had listened to our conversation.
(That day marked the first on my journey to de-Google and take serious steps preserve my privacy online)
It's great that you're focused in on privacy but that's not what's happening.
You can examine every byte of traffic off your phone. There isn't an open audio stream: it'd be too obvious. On phone analysis is too computationally intensive to be inobtrusive.
You're experiencing some combination of frequency illusion and priming when you experience these "phone listening in".
It is far more likely that you had seen the product advertised before but not consciously considered it (priming) followed by a discussion which made you more aware of it so you noticed the ads more (frequency bias).
The fact is companies don't even need to record your conversations to know how to get you to buy what they want you to buy.