[EKS] [request]: Project Bophades - Run EKS containers on AWS Lambda

### Community Note

* Please vote on this issue by adding a 👍 [reaction](https://blog.github.com/2016-03-10-add-reactions-to-pull-requests-issues-and-comments/) to the original issue to help the community and maintainers prioritize this request
* Please do not leave "+1" or "me too" comments, they generate extra noise for issue followers and do not help prioritize the request
* If you are interested in working on this issue or have submitted a pull request, please leave a comment

**Tell us about your request**
I want the option to run containers on AWS Lambda for a variety of reasons--quick capacity surges, easy cross-region container placement, and enforced ephemerality among them.

**Which service(s) is this request for?**
EKS, with a sprinkling of Lambda

**Tell us about the problem you're trying to solve. What are you trying to do, and why is it hard?**
I would like, in addition to the current option of running containers on Fargate (which still requires a bit of setup work per AWS account / region) to also have the option to instantiate workloads (either temporarily or steady-state) on AWS Lambda via its ability to support Docker containers as runtime images.

**Are you currently working around this issue?**
I am currently not using EKS and hoping to change that.

**Additional context**
I understand that this request may sound deranged, but it's not. I already do CI/CD deployments this way via Lambda + self-hosted GitHub Actions runners; the model works, and is orchestrated via Step Functions.

**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.)

Start by reviewing the existing EKS and Fargate container model alongside AWS Lambda's Docker-container runtime, including the temporary and steady-state use cases described here. Done would require a defined, supported way to place EKS workloads on Lambda, with the account, region, and orchestration behavior specified.

Written by the indexing model from the issue text.