> "Free" and "ad-supported" mean completely different things, and always have done.
"Free" in the context Amazon is using it (what Richard Stallman would refer to as Gratis) means that I do not have to pay money for something. That is a literal economic/dictionary definition.
Therefore, ad-supported in this context is a subset of "Free," as is any other form of non-monetary subsidization. So long as the end user is not paying, it is free.
The Free Software Foundation is free, but not ad-supported (though it strives to be free both in the sense "libre" (open/available) and "gratis" (not costing dollars).
If you show ads you're costing your users brain cycles and creating distraction and friction. The cost isn't monetary, but it's still a real indirect cost.
If it wasn't a real cost, ad-blockers would hardly be as popular as they are - and the ad industry wouldn't be quite so worried about them.
IMO the idea that anyone can believe the two models are identical from the user's point of view is not encouraging.
You're confusing something entirely different here. "Free" in "Free Software Foundation" is free as in freedom to use for any purpose[0][1], rather than free price. You should not use this example to argue whether "free price" implies "ad-free".
"Free" and "ad-supported" mean completely different things, and always have done.