[Bug] Brokers yield "Error Starting up in Worker" when functions are enabled

### Search before asking

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

### Version

Helm: 3.0
GKE: 1.27
Pulsar: 2.10.2

### Minimal reproduce step

Installing a pulsar cluster on GKE autopilot using the helm chart with mostly default settings.

### What did you expect to see?

A working cluster

### What did you see instead?

I'm getting an exception on my brokers initialization:
```
2023-12-19T00:47:53,609+0000 [main] INFO org.apache.pulsar.functions.utils.functions.FunctionUtils - Searching for functions in /pulsar/./functions
2023-12-19T00:47:53,610+0000 [main] WARN org.apache.pulsar.functions.utils.functions.FunctionUtils - Functions archive directory not found
2023-12-19T00:47:53,612+0000 [main] ERROR org.apache.pulsar.functions.worker.PulsarWorkerService - Error Starting up in worker
org.apache.pulsar.client.admin.PulsarAdminException: java.lang.IllegalStateException: Client instance has been closed.
at org.apache.pulsar.client.admin.internal.BaseResource.getApiException(BaseResource.java:251) ~[org.apache.pulsar-pulsar-client-admin-original-2.10.2.jar:2.10.2]
at org.apache.pulsar.client.admin.internal.BaseResource.sync(BaseResource.java:301) ~[org.apache.pulsar-pulsar-client-admin-original-2.10.2.jar:2.10.2]
at org.apache.pulsar.client.admin.internal.TopicsImpl.getSubscriptions(TopicsImpl.java:613) ~[org.apache.pulsar-pulsar-client-admin-original-2.10.2.jar:2.10.2]
at org.apache.pulsar.functions.worker.PulsarWorkerService.start(PulsarWorkerService.java:457) ~[org.apache.pulsar-pulsar-functions-worker-2.10.2.jar:2.10.2]
at org.apache.pulsar.broker.PulsarService.startWorkerService(PulsarService.java:1608) ~[org.apache.pulsar-pulsar-broker-2.10.2.jar:2.10.2]
at org.apache.pulsar.broker.PulsarService.start(PulsarService.java:795) ~[org.apache.pulsar-pulsar-broker-2.10.2.jar:2.10.2]
at org.apache.pulsar.PulsarBrokerStarter$BrokerStarter.start(PulsarBrokerStarter.java:273) ~[org.apache.pulsar-pulsar-broker-2.10.2.jar:2.10.2]
at org.apache.pulsar.PulsarBrokerStarter.main(PulsarBrokerStarter.java:350) ~[org.apache.pulsar-pulsar-broker-2.10.2.jar:2.10.2]
Caused by: java.lang.IllegalStateException: Client instance has been closed.
at org.glassfish.jersey.internal.guava.Preconditions.checkState(Preconditions.java:169) ~[org.glassfish.jersey.core-jersey-common-2.34.jar:?]
at org.glassfish.jersey.client.JerseyClient.checkNotClosed(JerseyClient.java:257) ~[org.glassfish.jersey.core-jersey-client-2.34.jar:?]
at org.glassfish.jersey.client.JerseyWebTarget.checkNotClosed(JerseyWebTarget.java:118) ~[org.glassfish.jersey.core-jersey-client-2.34.jar:?]
at org.glassfish.jersey.client.JerseyWebTarget.path(JerseyWebTarget.java:129) ~[org.glassfish.jersey.core-jersey-client-2.34.jar:?]
at org.glassfish.jersey.client.JerseyWebTarget.path(JerseyWebTarget.java:38) ~[org.glassfish.jersey.core-jersey-client-2.34.jar:?]
at org.apache.pulsar.client.admin.internal.TopicsImpl.topicPath(TopicsImpl.java:1319) ~[org.apache.pulsar-pulsar-client-admin-original-2.10.2.jar:2.10.2]
at org.apache.pulsar.client.admin.internal.TopicsImpl.getSubscriptionsAsync(TopicsImpl.java:619) ~[org.apache.pulsar-pulsar-client-admin-original-2.10.2.jar:2.10.2]
at org.apache.pulsar.client.admin.internal.TopicsImpl.lambda$getSubscriptions$20(TopicsImpl.java:613) ~[org.apache.pulsar-pulsar-client-admin-original-2.10.2.jar:2.10.2]
at org.apache.pulsar.client.admin.internal.BaseResource.sync(BaseResource.java:292) ~[org.apache.pulsar-pulsar-client-admin-original-2.10.2.jar:2.10.2]
... 6 more
2023-12-19T00:47:53,619+0000 [main] ERROR org.apache.pulsar.broker.PulsarService - Failed to start Pulsar service: org.apache.pulsar.client.admin.PulsarAdminException: java.lang.IllegalStateException: Client instance has been closed.
java.lang.RuntimeException: org.apache.pulsar.client.admin.PulsarAdminException: java.lang.IllegalStateException: Client instance has been closed.
at org.apache.pulsar.functions.worker.PulsarWorkerService.start(PulsarWorkerService.java:585) ~[org.apache.pulsar-pulsar-functions-worker-2.10.2.jar:2.10.2]
at org.apache.pulsar.broker.PulsarService.startWorkerService(PulsarService.java:1608) ~[org.apache.pulsar-pulsar-broker-2.10.2.jar:2.10.2]
at org.apache.pulsar.broker.PulsarService.start(PulsarService.java:795) ~[org.apache.pulsar-pulsar-broker-2.10.2.jar:2.10.2]
at org.apache.pulsar.PulsarBrokerStarter$BrokerStarter.start(PulsarBrokerStarter.java:273) ~[org.apache.pulsar-pulsar-broker-2.10.2.jar:2.10.2]
at org.apache.pulsar.PulsarBrokerStarter.main(PulsarBrokerStarter.java:350) ~[org.apache.pulsar-pulsar-broker-2.10.2.jar:2.10.2]
Caused by: org.apache.pulsar.client.admin.PulsarAdminException: java.lang.IllegalStateException: Client instance has been closed.
at org.apache.pulsar.client.admin.internal.BaseResource.getApiException(BaseResource.java:251) ~[org.apache.pulsar-pulsar-client-admin-original-2.10.2.jar:2.10.2]
at org.apache.pulsar.client.admin.internal.BaseResource.sync(BaseResource.java:301) ~[org.apache.pulsar-pulsar-client-admin-original-2.10.2.jar:2.10.2]
at org.apache.pulsar.client.admin.internal.TopicsImpl.getSubscriptions(TopicsImpl.java:613) ~[org.apache.pulsar-pulsar-client-admin-original-2.10.2.jar:2.10.2]
at org.apache.pulsar.functions.worker.PulsarWorkerService.start(PulsarWorkerService.java:457) ~[org.apache.pulsar-pulsar-functions-worker-2.10.2.jar:2.10.2]
... 4 more
Caused by: java.lang.IllegalStateException: Client instance has been closed.
at org.glassfish.jersey.internal.guava.Preconditions.checkState(Preconditions.java:169) ~[org.glassfish.jersey.core-jersey-common-2.34.jar:?]
at org.glassfish.jersey.client.JerseyClient.checkNotClosed(JerseyClient.java:257) ~[org.glassfish.jersey.core-jersey-client-2.34.jar:?]
at org.glassfish.jersey.client.JerseyWebTarget.checkNotClosed(JerseyWebTarget.java:118) ~[org.glassfish.jersey.core-jersey-client-2.34.jar:?]
at org.glassfish.jersey.client.JerseyWebTarget.path(JerseyWebTarget.java:129) ~[org.glassfish.jersey.core-jersey-client-2.34.jar:?]
at org.glassfish.jersey.client.JerseyWebTarget.path(JerseyWebTarget.java:38) ~[org.glassfish.jersey.core-jersey-client-2.34.jar:?]
at org.apache.pulsar.client.admin.internal.TopicsImpl.topicPath(TopicsImpl.java:1319) ~[org.apache.pulsar-pulsar-client-admin-original-2.10.2.jar:2.10.2]
at org.apache.pulsar.client.admin.internal.TopicsImpl.getSubscriptionsAsync(TopicsImpl.java:619) ~[org.apache.pulsar-pulsar-client-admin-original-2.10.2.jar:2.10.2]
at org.apache.pulsar.client.admin.internal.TopicsImpl.lambda$getSubscriptions$20(TopicsImpl.java:613) ~[org.apache.pulsar-pulsar-client-admin-original-2.10.2.jar:2.10.2]
at org.apache.pulsar.client.admin.internal.BaseResource.sync(BaseResource.java:292) ~[org.apache.pulsar-pulsar-client-admin-original-2.10.2.jar:2.10.2]
at org.apache.pulsar.client.admin.internal.TopicsImpl.getSubscriptions(TopicsImpl.java:613) ~[org.apache.pulsar-pulsar-client-admin-original-2.10.2.jar:2.10.2]
at org.apache.pulsar.functions.worker.PulsarWorkerService.start(PulsarWorkerService.java:457) ~[org.apache.pulsar-pulsar-functions-worker-2.10.2.jar:2.10.2]
... 4 more
2023-12-19T00:47:53,620+0000 [pulsar-service-shutdown] INFO org.apache.pulsar.broker.PulsarService - Closing PulsarService
2023-12-19T00:47:53,621+0000 [main] ERROR org.apache.pulsar.PulsarBrokerStarter - Failed to start pulsar service.
org.apache.pulsar.broker.PulsarServerException: java.lang.RuntimeException: org.apache.pulsar.client.admin.PulsarAdminException: java.lang.IllegalStateException: Client instance has been closed.
at org.apache.pulsar.broker.PulsarService.start(PulsarService.java:827) ~[org.apache.pulsar-pulsar-broker-2.10.2.jar:2.10.2]
at org.apache.pulsar.PulsarBrokerStarter$BrokerStarter.start(PulsarBrokerStarter.java:273) ~[org.apache.pulsar-pulsar-broker-2.10.2.jar:2.10.2]
at org.apache.pulsar.PulsarBrokerStarter.main(PulsarBrokerStarter.java:350) ~[org.apache.pulsar-pulsar-broker-2.10.2.jar:2.10.2]
Caused by: java.lang.RuntimeException: org.apache.pulsar.client.admin.PulsarAdminException: java.lang.IllegalStateException: Client instance has been closed.
at org.apache.pulsar.functions.worker.PulsarWorkerService.start(PulsarWorkerService.java:585) ~[org.apache.pulsar-pulsar-functions-worker-2.10.2.jar:2.10.2]
at org.apache.pulsar.broker.PulsarService.startWorkerService(PulsarService.java:1608) ~[org.apache.pulsar-pulsar-broker-2.10.2.jar:2.10.2]
at org.apache.pulsar.broker.PulsarService.start(PulsarService.java:795) ~[org.apache.pulsar-pulsar-broker-2.10.2.jar:2.10.2]
... 2 more
Caused by: org.apache.pulsar.client.admin.PulsarAdminException: java.lang.IllegalStateException: Client instance has been closed.
at org.apache.pulsar.client.admin.internal.BaseResource.getApiException(BaseResource.java:251) ~[org.apache.pulsar-pulsar-client-admin-original-2.10.2.jar:2.10.2]
at org.apache.pulsar.client.admin.internal.BaseResource.sync(BaseResource.java:301) ~[org.apache.pulsar-pulsar-client-admin-original-2.10.2.jar:2.10.2]
at org.apache.pulsar.client.admin.internal.TopicsImpl.getSubscriptions(TopicsImpl.java:613) ~[org.apache.pulsar-pulsar-client-admin-original-2.10.2.jar:2.10.2]
at org.apache.pulsar.functions.worker.PulsarWorkerService.start(PulsarWorkerService.java:457) ~[org.apache.pulsar-pulsar-functions-worker-2.10.2.jar:2.10.2]
at org.apache.pulsar.broker.PulsarService.startWorkerService(PulsarService.java:1608) ~[org.apache.pulsar-pulsar-broker-2.10.2.jar:2.10.2]
at org.apache.pulsar.broker.PulsarService.start(PulsarService.java:795) ~[org.apache.pulsar-pulsar-broker-2.10.2.jar:2.10.2]
... 2 more
Caused by: java.lang.IllegalStateException: Client instance has been closed.
at org.glassfish.jersey.internal.guava.Preconditions.checkState(Preconditions.java:169) ~[org.glassfish.jersey.core-jersey-common-2.34.jar:?]
at org.glassfish.jersey.client.JerseyClient.checkNotClosed(JerseyClient.java:257) ~[org.glassfish.jersey.core-jersey-client-2.34.jar:?]
at org.glassfish.jersey.client.JerseyWebTarget.checkNotClosed(JerseyWebTarget.java:118) ~[org.glassfish.jersey.core-jersey-client-2.34.jar:?]
at org.glassfish.jersey.client.JerseyWebTarget.path(JerseyWebTarget.java:129) ~[org.glassfish.jersey.core-jersey-client-2.34.jar:?]
at org.glassfish.jersey.client.JerseyWebTarget.path(JerseyWebTarget.java:38) ~[org.glassfish.jersey.core-jersey-client-2.34.jar:?]
at org.apache.pulsar.client.admin.internal.TopicsImpl.topicPath(TopicsImpl.java:1319) ~[org.apache.pulsar-pulsar-client-admin-original-2.10.2.jar:2.10.2]
at org.apache.pulsar.client.admin.internal.TopicsImpl.getSubscriptionsAsync(TopicsImpl.java:619) ~[org.apache.pulsar-pulsar-client-admin-original-2.10.2.jar:2.10.2]
at org.apache.pulsar.client.admin.internal.TopicsImpl.lambda$getSubscriptions$20(TopicsImpl.java:613) ~[org.apache.pulsar-pulsar-client-admin-original-2.10.2.jar:2.10.2]
at org.apache.pulsar.client.admin.internal.BaseResource.sync(BaseResource.java:292) ~[org.apache.pulsar-pulsar-client-admin-original-2.10.2.jar:2.10.2]
at org.apache.pulsar.client.admin.internal.TopicsImpl.getSubscriptions(TopicsImpl.java:613) ~[org.apache.pulsar-pulsar-client-admin-original-2.10.2.jar:2.10.2]
at org.apache.pulsar.functions.worker.PulsarWorkerService.start(PulsarWorkerService.java:457) ~[org.apache.pulsar-pulsar-functions-worker-2.10.2.jar:2.10.2]
at org.apache.pulsar.broker.PulsarService.startWorkerService(PulsarService.java:1608) ~[org.apache.pulsar-pulsar-broker-2.10.2.jar:2.10.2]
at org.apache.pulsar.broker.PulsarService.start(PulsarService.java:795) ~[org.apache.pulsar-pulsar-broker-2.10.2.jar:2.10.2]
... 2 more
```

### Anything else?

If I disable functions using the Helm chart values, the brokers initializer correctly.

### Are you willing to submit a PR?

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

Start with PulsarWorkerService.start at the reported call to TopicsImpl.getSubscriptions, then trace PulsarService.startWorkerService during broker startup. Reproduce the Helm deployment on GKE with functions enabled and determine why the admin client is closed; done means the broker starts successfully without the reported worker exception.

Written by the indexing model from the issue text.