[EKS] [request]: Expose CoreDNS liveness probe configuration for self-managed deployments

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**Tell us about your request**
Expose CoreDNS liveness/readiness probe configuration through EKS management APIs, similar to how other system components can be configured.

**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?**

High-frequency microservices need faster DNS failure detection (failureThreshold: 1)

```bash
# Enable CoreDNS add-on with custom liveness probe configuration
aws eks create-addon --cluster-name my-cluster --addon-name coredns \
--configuration-values '{
"deployment": {
"livenessProbe": {
"failureThreshold": 1,
"timeoutSeconds": 5,
"periodSeconds": 10,
"initialDelaySeconds": 30
}
}
}'

# Update existing add-on
aws eks update-addon --cluster-name my-cluster --addon-name coredns \
--configuration-values '{
"deployment": {
"livenessProbe": {"failureThreshold": 1}
}
}' \
--resolve-conflicts OVERWRITE
```

**Terraform Configuration:**
```hcl
resource "aws_eks_addon" "coredns" {
cluster_name = aws_eks_cluster..name
addon_name = "coredns"

configuration_values = jsonencode({
deployment = {
livenessProbe = {
failureThreshold = 1
timeoutSeconds = 5
periodSeconds = 10
initialDelaySeconds = 30
}
}
})
}
```

**Are you currently working around this issue?**
Manual patches with drift-correction controllers

**Additional context**
- Kubernetes version: 1.33
- Platform version: eks.6

This is an EKS feature request, and the issue names no repository files, tests, or implementation entry points. Start by reviewing the EKS add-on configuration APIs and the CoreDNS add-on behavior described here. Done means self-managed CoreDNS deployments can configure liveness and readiness probes through EKS management APIs without manual patches or drift.

Written by the indexing model from the issue text.