I find it very ironic that AWS is behind this. Whenever I buy books from Amazon I am amazed at their broken search engines. Just search a topic on Amazon and then try to sort the results. LOL.
IIRC, most of that infrastructure is/was Oracle based and much of it going to another DB. I'm not sure if Elastic is even in the mix, or how well it scales to Amazon's levels.
Given the age of the offering, it might actually be the CloudSearch [0] product that is used by the Amazon.com search team.
FWIW, I've always found the Amazon store search to be pretty decent; normally I don't use a website's built in search system, opting for Google instead.