[EKS Auto Mode] [Feature Request]: Support BYOIP EIP pool assignment for public node classes

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**Tell us about your request**

Support BYOIP EIP pool assignment for Auto Mode public node classes

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

EKS Auto Mode

**Tell us about the problem you're trying to solve. What are you trying to do, and why is it hard?**

Auto Mode public node classes currently only support AWS-assigned public IPs via `associatePublicIpAddress`. There is no way to specify a BYOIP EIP allocation pool so that nodes receive a static, customer-owned IP on launch.

Additionally, `ec2:AssociateAddress` is blocked on Auto Mode node ENIs via a resource-based IAM deny, making it impossible to assign EIPs through a user-deployed controller as a workaround.

**Are you currently working around this issue?**

Using self-managed nodes within an Auto Mode cluster, which requires manually providing kube-proxy, CoreDNS, and kubelet CSR approval — components that Auto Mode otherwise handles transparently.

**Additional context**

The requested behavior: allow `NodeClass` to reference a BYOIP EIP allocation pool (e.g., via an `eipPool` or `allocationIds` field). Auto Mode would assign an available EIP from that pool on node launch and release it on termination.

Start by reading the NodeClass and EKS Auto Mode public node class behavior described in the issue, along with the BYOIP EIP allocation and release requirements. No repository files or tests are named; done means a NodeClass can reference an EIP pool, assign an available EIP at node launch, and release it at termination.

Written by the indexing model from the issue text.