[EKS] [OIDC]: OIDC response URL

### 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**
The new dual-stack compatible endpoint for the OIDC issuer URL (mentioned here - https://github.com/aws/containers-roadmap/issues/2038#issuecomment-2278450601) returns `eks.region.amazonaws.com` URLs instead of `oidc-eks.region.api.aws`.

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

**Tell us about the problem you're trying to solve. What are you trying to do, and why is it hard?**
Make OIDC work together with the EKS private endpoint.

**Are you currently working around this issue?**
Not using the EKS private endpoint.

Start with the dual-stack OIDC issuer URL described in the issue and the linked EKS roadmap comment, then compare its behavior with the EKS private endpoint requirement. Done means OIDC works with the EKS private endpoint while returning the expected compatible issuer URL.

Written by the indexing model from the issue text.