[Bug] Websocket connection closed

### Search before asking

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

### Version

v3.1.1

### Minimal reproduce step

Try to produce in Websocket

### What did you expect to see?

A message produced

### What did you see instead?

````2023-11-27T17:18:28,518+0000 [pulsar-external-web-5-15] WARN org.apache.pulsar.websocket.ReaderHandler - [78.242.0.0:40693] Failed in creating reader on topic non-persistent://tenant/pulsar_1/profile
org.apache.pulsar.client.api.PulsarClientException$LookupException: {"errorMsg":"org.apache.pulsar.client.api.PulsarClientException: Connection already closed","reqId":3472645042792490684, "remote":"pulsar.com/91.208.0.0:6650", "local":"/10.2.0.0:44840"}
at org.apache.pulsar.client.api.PulsarClientException.unwrap(PulsarClientException.java:1053) ~[org.apache.pulsar-pulsar-client-api-3.1.1.jar:3.1.1]
at org.apache.pulsar.client.impl.ReaderBuilderImpl.create(ReaderBuilderImpl.java:78) ~[org.apache.pulsar-pulsar-client-original-3.1.1.jar:3.1.1]
at org.apache.pulsar.websocket.ReaderHandler.(ReaderHandler.java:112) ~[org.apache.pulsar-pulsar-websocket-3.1.1.jar:3.1.1]
at org.apache.pulsar.websocket.WebSocketReaderServlet.lambda$configure$0(WebSocketReaderServlet.java:44) ~[org.apache.pulsar-pulsar-websocket-3.1.1.jar:3.1.1]
at org.eclipse.jetty.websocket.server.WebSocketServerFactory.acceptWebSocket(WebSocketServerFactory.java:275) ~[org.eclipse.jetty.websocket-websocket-server-9.4.51.v20230217.jar:9.4.51.v20230217]
at org.eclipse.jetty.websocket.server.WebSocketServerFactory.acceptWebSocket(WebSocketServerFactory.java:260) ~[org.eclipse.jetty.websocket-websocket-server-9.4.51.v20230217.jar:9.4.51.v20230217]
at org.eclipse.jetty.websocket.servlet.WebSocketServlet.service(WebSocketServlet.java:160) ~[org.eclipse.jetty.websocket-websocket-servlet-9.4.51.v20230217.jar:9.4.51.v20230217]
```

### Anything else?

on client side
```>Error 500 Failed to create producer/consumer: {"errorMsg":"org.apache.pulsar.client.api.PulsarClientException: Connection already closed","reqId":2689535377619156521, "remote":"pulsar.com/91.208.0.0:6650", "local":"/10.2.0.0:52584"}\n\n

HTTP ERROR 500 Failed to create producer/consumer: {"errorMsg":"org.apache.pulsar.client.api.PulsarClientException: Connection already closed","reqId":2689535377619156521, "remote":"pulsar.com/91.208.0.0:6650", "local":"/10.2.0.0:52584"}

\n\n\n\n\n\nURI:/ws/v2/producer/persistent/tenant/pulsar_1/ttopicSTATUS:500MESSAGE:Failed to create producer/consumer: {"errorMsg":"org.apache.pulsar.client.api.PulsarClientException: Connection already closed","reqId":2689535377619156521, "remote":"pulsar.com/91.208.0.0:6650", "local":"/10.2.0.0:52584"}SERVLET:org.apache.pulsar.websocket.WebSocketProducerServlet-38cedb7d\n

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### Are you willing to submit a PR?

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

Start with the WebSocket stack trace, especially ReaderHandler.java:112, WebSocketReaderServlet.java:44, ReaderBuilderImpl.java:78, and the WebSocketProducerServlet entry point shown in the error. Reproduce the producer or reader request on Pulsar v3.1.1 and trace why the connection closes; done means the WebSocket creates the producer or consumer and produces a message without the HTTP 500 error.

Written by the indexing model from the issue text.