[EKS] [Automate CoreDNS Patching on Fargate]: Automate patching of compute-type from ec2 to fargate

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**Tell us about your request**
What do you want us to build?

Please make it so if CoreDNS is running on a Fargate Node it can be automatically patched in the Control Plane to be `compute-type`: Fargate. I believe this could be done at the Deployment or Pod Level.

**Which service(s) is this request for?**

This should be for Fargate on EKS.

**Tell us about the problem you're trying to solve. What are you trying to do, and why is it hard?**
What outcome are you trying to achieve, ultimately, and why is it hard/impossible to do right now? What is the impact of not having this problem solved? The more details you can provide, the better we'll be able to understand and solve the problem.

Please see attachments.

**Are you currently working around this issue?**
We patch the deployment manually.

**Additional context**
N/A

**Attachments**
If you think you might have additional information that you'd like to include via an attachment, please do - we'll take a look. (Remember to remove any personally-identifiable information.)

https://docs.aws.amazon.com/prescriptive-guidance/latest/patterns/deploy-coredns-on-amazon-eks-with-fargate-automatically-using-terraform-and-python.html

https://github.com/hashicorp/terraform-provider-aws/issues/11327

https://www.reddit.com/r/Terraform/comments/vrm8ol/eks_coredns_still_requires_a_patch_to_remove_the/

https://andyhunt.me/til/2021/03/29/coredns-does-not-run-on-aws-fargate-by-default/

No repository files, tests, or implementation entry points are named. Start by reviewing the requested EKS Fargate CoreDNS behavior and the linked AWS guidance and Terraform provider issue; done means CoreDNS is automatically patched to compute-type Fargate without manually patching its deployment.

Written by the indexing model from the issue text.