Flaky-test: ProxyAuthenticationTest.authenticatedSocketTest

### Search before asking

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

### Example failure

https://github.com/apache/pulsar/actions/runs/3581022993/jobs/6023785454#step:10:703

### Exception stacktrace

Full exception stacktrace

Error:  Tests run: 27, Failures: 1, Errors: 0, Skipped: 25, Time elapsed: 46.332 s <<< FAILURE! - in org.apache.pulsar.websocket.proxy.ProxyAuthenticationTest

  Error:  authenticatedSocketTest(org.apache.pulsar.websocket.proxy.ProxyAuthenticationTest)  Time elapsed: 10.037 s  <<< FAILURE!

  org.testng.internal.thread.ThreadTimeoutException: Method org.apache.pulsar.websocket.proxy.ProxyAuthenticationTest.authenticatedSocketTest() didn't finish within the time-out 10000

  	at java.base@17.0.5/java.lang.Thread.sleep(Native Method)

  	at java.base@17.0.5/java.lang.Thread.sleep(Thread.java:337)

  	at java.base@17.0.5/java.util.concurrent.TimeUnit.sleep(TimeUnit.java:446)

  	at app//org.awaitility.core.Uninterruptibles.sleepUninterruptibly(Uninterruptibles.java:35)

  	at app//org.awaitility.core.ConditionAwaiter.await(ConditionAwaiter.java:117)

  	at app//org.awaitility.core.AssertionCondition.await(AssertionCondition.java:119)

  	at app//org.awaitility.core.AssertionCondition.await(AssertionCondition.java:31)

  	at app//org.awaitility.core.ConditionFactory.until(ConditionFactory.java:985)

  	at app//org.awaitility.core.ConditionFactory.untilAsserted(ConditionFactory.java:769)

  	at app//org.apache.pulsar.websocket.proxy.ProxyAuthenticationTest.checkSocket(ProxyAuthenticationTest.java:133)

  	at app//org.apache.pulsar.websocket.proxy.ProxyAuthenticationTest.authenticatedSocketTest(ProxyAuthenticationTest.java:144)

  	at java.base@17.0.5/jdk.internal.reflect.NativeMethodAccessorImpl.invoke0(Native Method)

  	at java.base@17.0.5/jdk.internal.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:77)

  	at java.base@17.0.5/jdk.internal.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)

  	at java.base@17.0.5/java.lang.reflect.Method.invoke(Method.java:568)

  	at app//org.testng.internal.invokers.MethodInvocationHelper.invokeMethod(MethodInvocationHelper.java:139)

  	at app//org.testng.internal.invokers.InvokeMethodRunnable.runOne(InvokeMethodRunnable.java:47)

  	at app//org.testng.internal.invokers.InvokeMethodRunnable.call(InvokeMethodRunnable.java:76)

  	at app//org.testng.internal.invokers.InvokeMethodRunnable.call(InvokeMethodRunnable.java:11)

  	at java.base@17.0.5/java.util.concurrent.FutureTask.run(FutureTask.java:264)

  	at java.base@17.0.5/java.util.concurrent.ThreadPoolExecutor.runWorker(ThreadPoolExecutor.java:1136)

  	at java.base@17.0.5/java.util.concurrent.ThreadPoolExecutor$Worker.run(ThreadPoolExecutor.java:635)

  	at java.base@17.0.5/java.lang.Thread.run(Thread.java:833)

### Are you willing to submit a PR?

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

Start with the linked GitHub Actions failure and the ProxyAuthenticationTest.authenticatedSocketTest method, especially checkSocket at ProxyAuthenticationTest.java:133 and the caller at line 144. Reproduce the timeout and determine why the authenticated socket does not complete within 10 seconds; done means the test runs reliably without the reported timeout.

Written by the indexing model from the issue text.