Not sure what you mean by shopping API, but here is all that their affiliate program policies[0] say about price comparisons with other sites:
> 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.
I meant advertising API. Perhaps they have updated their terms for the advertising API, as it appears their affiliate program does allow price comparison now. I believe that was not the case previously.
They have poor naming. There is an Advertising API, and then there's a Product Advertising API which is often called the Product API.
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.
> 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