Bottlerocket fails to find DNS name in private subnet

**Image I'm using:** Bottlerocket OS 1.13.4 (aws-k8s-1.26)

**What I expected to happen:** AWS instance has two subnets, a public subnet and a private subnet (without a NAT gateway)

**What actually happened:**
```
[ 36.677435] sundog[1152]: Setting generator 'pluto private-dns-name' failed with exit code 1 - stderr: Error describing instance 'i-0c59419f023b394ba': dispatch failure: timeout: error trying to connect: HTTP connect timeout occurred after 3.1s: HTTP connect timeout occurred after 3.1s: timed out (DispatchFailure(DispatchFailure { source: ConnectorError { kind: Timeout, source: hyper::Error(Connect, HttpTimeoutError { kind: "HTTP connect", duration: 3.1s }) } }))
[FAILED] Failed to start User-specified setting generators.
See 'systemctl status sundog.service' for details.
```

**How to reproduce the problem:** Try to launch an EKS cluster with Bottlerocket for EKS 1.26 with two subnets, one public and one private.

DHCP options for the subnets:

Example eksctl config:

```
apiVersion: eksctl.io/v1alpha5
kind: ClusterConfig

metadata:
name: why-wont-this-work
region: us-east-2
version: '1.26'

vpc:
clusterEndpoints:
publicAccess: true
privateAccess: true
id: "vpc-caf3bab3"
subnets:
public:
pub-us-east-2a:
id: "subnet-0000111"
private:
priv-us-east-2a:
id: "subnet-0000222"

iam:
withOIDC: true

nodeGroups:
- name: east2a
instanceType: m7g.xlarge
amiFamily: Bottlerocket
privateNetworking: true
iam:
attachPolicyARNs:
- arn:aws:iam::aws:policy/AmazonEKSWorkerNodePolicy
- arn:aws:iam::aws:policy/ElasticLoadBalancingFullAccess
- arn:aws:iam::aws:policy/AmazonSSMManagedInstanceCore
- arn:aws:iam::aws:policy/AmazonEKS_CNI_Policy
- arn:aws:iam::aws:policy/AmazonEC2ContainerRegistryReadOnly
withAddonPolicies:
autoScaler: true
cloudWatch: false
externalDNS: true
maxSize: 4
subnets:
- pub-us-east-2a
- priv-us-east-2a
labels:
env: prod
desiredCapacity: 1
```

Full boot log: https://gist.github.com/robd003/7f05a5f76bf241f047a99ab3135f6a03