aws-sigv4-proxy-admission-controller - failed to call webhook

**Describe the bug**
Unable to install the "aws-sigv4-proxy-admission-controller" helm chart. The pods are not getting created. The events show the warning message `"failed to call webhook: Post https://aws-sigv4-proxy-admission-controller-webhook-service.kube-system.svc:443/mutate?timeout=10s`.

**Steps to reproduce**
```sh
helm upgrade -i aws-sigv4-proxy-admission-controller \
eks/aws-sigv4-proxy-admission-controller \
--namespace kube-system

Release "aws-sigv4-proxy-admission-controller" does not exist. Installing it now.
NAME: aws-sigv4-proxy-admission-controller
LAST DEPLOYED: Mon Aug 8 19:50:30 2022
NAMESPACE: kube-system
STATUS: deployed
REVISION: 1
TEST SUITE: None
NOTES:
aws-sigv4-proxy-admission-controller has been installed or updated. To check the status of pods, run:
kubectl get pods -n kube-system
```

```sh
k get events -n kube-system -w

0s Warning FailedCreate replicaset/aws-sigv4-proxy-admission-controller-webhook-deployment-69689b75d7 Error creating: Internal error occurred: failed calling webhook "aws-sigv4-proxy-admission-controller.k8s.aws": failed to call webhook: Post "https://aws-sigv4-proxy-admission-controller-webhook-service.kube-system.svc:443/mutate?timeout=10s": no endpoints available for service "aws-sigv4-proxy-admission-controller-webhook-service"
```

**Expected outcome**
Helm chart successfully installed.

**Environment**

* Chart name: aws-sigv4-proxy-admission-controller
* Chart version: 0.1.2
* Kubernetes version: 1.22
* Using EKS (yes/no), if so version? Yes, and eks.5 (Fargate Cluster)

**Additional Context**:
I can install the controller by rendering the manifests, apply all except the MutatingWebhookConfiguration, wait for the pod to be running, and apply the webhook.

```sh
helm template eks/aws-sigv4-proxy-admission-controller > sigv4-proxy.yaml
```

Start by reproducing the Helm installation for chart version 0.1.2 on Kubernetes 1.22, then render the manifests with `helm template` as shown. Inspect the MutatingWebhookConfiguration, webhook service, and controller deployment ordering; done means a normal Helm install creates the controller pods without the no-endpoints webhook error.

Written by the indexing model from the issue text.