It is against the amazon shopping api terms of service to offer price comparison. So they haven't probably for that reason.
> if you choose to display prices for any Product on your Site in any “comparison” format (including through the use of any price-comparison tool or engine) together with prices for the same or similar products offered through any web site or other means other than an Amazon Site, you must display both the lowest “new” price and, if we provide it to you, the lowest “used” price at which the Product is available on the Amazon Site.
[0] https://affiliate-program.amazon.com/help/operating/policies
The Advertising API is for advertisers running ads with Amazon Advertising. Apparently they don't allow certain competitors (shopping sites, comparison sites, ad networks) to use it: https://advertising.amazon.com/en-us/resources/ad-policy/api
The Product API is for affiliates to fetch product/price information in a reliable way instead of scraping the main site for it. I don't think they've ever prohibited price comparison sites. The last time I really looked into it was several years ago, and they weren't restricted at that point either.