Well, no such thing as the ‘same search’ anymore. Amazon, and a lot of other things, use a LOT of ‘AI’ and prior history data to ‘customize’ the results for each user. Effectively the website is ‘different’ for every user, every time.

Different browsers? Almost certainly different cookie histories on the iMac vs your Window PC.

Is there a Kindle reader app installed on the iMac?

Within an Amazon search session it is possible that Amazon is also further customizing the search parameters based on something the user did, or did not do, while perusing around.

Beyond that, I could not say specifically what thing must be changed to allow Amazon search to present the discounted ebook on the iMac. Other than manually editing the URL