Run kubernetes container stack on premise not connected to Internet/AWS.

Please take a look at this - https://aws.amazon.com/eks/eks-anywhere/faqs/

This question in the FAQ answers your question:

Q: Does EKS Anywhere require internet connectivity to an AWS region?

There are three connectivity options: fully connected, partially disconnected, and fully disconnected. For fully connected and partially disconnected connectivity, you can connect your Amazon EKS Anywhere clusters to AWS. This lets you leverage the EKS console as a single pane of glass for clusters running anywhere starting today, with future support for integrating with App Mesh, pushing logs and metrics into AWS for centralized observability, performing cluster backups and snapshots to Amazon S3 buckets, running cluster cost management and optimization tools, and running compliance checks, audit trail reporting, and configuration policy enforcement. In the case of partially disconnected clusters, there is no impact on your applications running on the clusters but since intermittent disconnects can last several hours, features like the EKS console in the AWS console will show state from the time of disconnect, with eventual consistency restored once the connection returns. In disconnected scenarios, you can use EKS Distro and leverage open source tools to run your clusters.