I agree that if Amazon or Google were not at all concerned about the product or service they deliver to their customers, but were instead a cover for some espionage group, they probably could build something like you describe using currently available technology. Whether it would be possible to hide from people looking for it is questionable.
And for a company like Google or Amazon, there is little to no incentive to do this as the benefit over monitoring just queries is marginal at best from an advertising perspective and could easily backfire and cost public support.
If we are in agreement that this isn’t actually happening or practical, but you are just pointing out that it would be theoretically possible, then sure, I agree.