EKS Anywhere - manage cluster without provider

I apologize, but there seems to be a misunderstanding in your question. While Amazon EKS Anywhere does support running Kubernetes clusters on-premises, it does not directly support installing on Red Hat Enterprise Linux (RHEL) machines without using a supported provider.

Amazon EKS Anywhere is designed to work with specific infrastructure providers. The supported providers include VMware vSphere, bare metal (via Tinkerbell), Nutanix, Apache CloudStack, and AWS Snow Family devices. It's not designed to be installed directly on individual Linux machines like RHEL without one of these underlying infrastructure providers.

If you want to use EKS Anywhere, you would need to choose one of the supported providers as the foundation for your deployment. For example, if you have a bare metal environment, you could use the Tinkerbell provider to set up EKS Anywhere on your physical machines.

It's important to note that EKS Anywhere is built on the Kubernetes Cluster API (CAPI) project, which relies on these providers to manage the full lifecycle of the machines in an EKS Anywhere cluster.

If you're looking to run Kubernetes on your RHEL machines without using one of the supported EKS Anywhere providers, you might want to consider other options like using Amazon EKS Distro directly or exploring alternative Kubernetes distributions that can be installed directly on Linux machines.
Sources
Kubernetes concepts - Amazon EKS
Amazon Elastic Kubernetes Service - Overview of Deployment Options on AWS
Deploy Amazon EKS clusters across cloud and on-premises environments - Amazon EKS