How do I store variables in S3 and access them from a KS test script?

If you are going to bother yourself working on AWS SDK, please go through the AWS tutorials first.

Once you have got familiar with AWS SDK for S3, then you want to configure your Katalon Studio project so that it has all required extenal dependencies (jar files) in the Drivers folder. Katalon Studio does NOT support resolving dependencies for S3 out of box. You need to resolve it yourself. The following post explains how to do it.