[Bug] pulsar-proxy Liveness probe failed: HTTP probe failed with statuscode: 401

### Search before asking

- [X] I searched in the [issues](https://github.com/apache/pulsar/issues) and found nothing similar.

### Version

kubernetes：1.28.4
pulsar-helm-chart：3.2.0
apachepulsar/pulsar-all：3.1.2

### Minimal reproduce step

1. `helm install pulsar --values charts/pulsar/values.yaml --set initialize=true --namespace pulsar pulsar-3.2.0.tgz`
2. `kubectl get pod -n pulsar`
3. `kubectl describe`

### What did you expect to see?

All pods are in running state

### What did you see instead?

`kubectl get pod -n pulsar` output
```
NAME READY STATUS RESTARTS AGE
pulsar-bookie-0 1/1 Running 0 11m
pulsar-bookie-1 1/1 Running 0 11m
pulsar-bookie-2 1/1 Running 0 11m
pulsar-broker-0 1/1 Running 2 (4m30s ago) 11m
pulsar-broker-1 1/1 Running 3 (3m42s ago) 11m
pulsar-broker-2 1/1 Running 3 (3m42s ago) 11m
pulsar-proxy-0 0/1 Running 1 (1s ago) 11m
pulsar-proxy-1 0/1 Running 1 (8s ago) 11m
pulsar-proxy-2 0/1 Running 1 (9s ago) 11m
pulsar-pulsar-init-7n2jz 0/1 Completed 0 11m
pulsar-pulsar-manager-7887f99f77-cc9q2 1/1 Running 0 11m
pulsar-recovery-0 1/1 Running 0 11m
pulsar-toolset-0 1/1 Running 0 11m
pulsar-zookeeper-0 1/1 Running 0 11m
pulsar-zookeeper-1 1/1 Running 0 11m
pulsar-zookeeper-2 1/1 Running 0 11m
```
`kubectl describe ` outpu：

```
Warning Unhealthy 3s (x7 over 63s) kubelet Liveness probe failed: HTTP probe failed with statuscode: 401
Warning Unhealthy 3s (x8 over 63s) kubelet Readiness probe failed: HTTP probe failed with statuscode: 401
```

**Modified on default basis values.yaml**
````yaml
namespace: "pulsar"
persistence: true
volumes:
persistence: true
local_storage: true

components:
# zookeeper
zookeeper: true
# bookkeeper
bookkeeper: true
# bookkeeper - autorecovery
autorecovery: true
# broker
broker: true
# functions
functions: true
# proxy
proxy: true
# toolset
toolset: true
# pulsar manager
pulsar_manager: true

# uses chart's appVersion when unspecified
defaultPulsarImageTag: 3.1.2

auth:
authentication:
enabled: true
provider: "jwt"
jwt:
# Enable JWT authentication
# If the token is generated by a secret key, set the usingSecretKey as true.
# If the token is generated by a private key, set the usingSecretKey as false.
usingSecretKey: false
authorization:
enabled: true
superUsers:
# broker to broker communication
broker: "broker-admin"
# proxy to broker communication
proxy: "proxy-admin"
# pulsar-admin client to broker/proxy communication
client: "admin"
# omits the above proxy role from superusers on the proxy
# and configures it as a proxy role on the broker in addition to the superusers
useProxyRoles: true

zookeeper:
podMonitor:
enabled: false
nodeSelector:
node-role.kubernetes.io/pulsar: pulsar
volumes:
persistence: true
data:
name: data
size: 100Gi
local_storage: true

bookkeeper:
podMonitor:
enabled: false
nodeSelector:
node-role.kubernetes.io/pulsar: pulsar
volumes:
persistence: true
journal:
name: journal
size: 100Gi
local_storage: true
ledgers:
name: ledgers
size: 100Gi
local_storage: true

autorecovery:
podMonitor:
enabled: false
nodeSelector:
node-role.kubernetes.io/pulsar: pulsar

broker:
podMonitor:
enabled: false
nodeSelector:
node-role.kubernetes.io/pulsar: pulsar

functions:
component: functions-worker
useBookieAsStateStore: true

proxy:
podMonitor:
enabled: false
nodeSelector:
node-role.kubernetes.io/pulsar: pulsar

dashboard:
nodeSelector:
node-role.kubernetes.io/pulsar: pulsar

toolset:
nodeSelector:
node-role.kubernetes.io/pulsar: pulsar

# 关闭监控组件
kube-prometheus-stack:
enabled: false

pulsar_manager:
nodeSelector:
node-role.kubernetes.io/pulsar: pulsar
admin:
user: pulsar_manager
password: zR7yF5fH
configData:
REDIRECT_HOST: "http://127.0.0.1"
REDIRECT_PORT: "9527"
DRIVER_CLASS_NAME: org.postgresql.Driver
URL: jdbc:postgresql://postgresql-ha-pgpool:5432/pulsar_manager
LOG_LEVEL: DEBUG
JWT_TOKEN:
```

### Anything else?

_No response_

### Are you willing to submit a PR?

- [X] I'm willing to submit a PR!

Start with charts/pulsar/values.yaml and the proxy liveness and readiness probe configuration, then reproduce the installation with the reported authentication settings and inspect the proxy with kubectl describe. Trace why the probes receive HTTP 401 when JWT authentication is enabled. Done means the proxy probes succeed and all Pulsar pods report ready without repeated restarts.

Written by the indexing model from the issue text.