Thank you for your interest in jsreport.

Can you please advice if it is sufficient to have one-time enterprise license for production environment. (consider there are 3 worker nodes running on the AWS cluster).

Unfortunately no. It isn't sufficient. Every jsreport instance needs an explicit license. If you run a cluster of multiple instances, you typically use the scale license.

Assume it is one time enterprise license, then how can we differentiate staging environment from the production since we deploy the same application in two environments.

https://jsreport.net/learn/faq#how-to-apply-license-key
You will put to the staging instances extra configuration. This will mark them as development and jsreport won't be validating parallel usage of the same license key.