### Description

The new [readiness port](https://www.elastic.co/guide/en/elasticsearch/reference/8.4/advanced-configuration.html#readiness-tcp-port) makes readiness checks on Kubernetes much easier. However the current implementation only allows connections through localhost. TCP probes on Kubernetes are run by the kubelet which is a process running on the Kubernetes node (and not from within the container or the Pod). The [Kubernetes documentation](https://kubernetes.io/docs/tasks/configure-pod-container/configure-liveness-readiness-startup-probes/#tcp-probes) mentions it, but it is kind of subtle: 

> For a TCP probe, the kubelet makes the probe connection at the node, not in the pod, which means that you can not use a service name in the host parameter since the kubelet is unable to resolve it.


That means a standard Kubernetes readiness probe cannot be used for Elasticsearch:
```
          readinessProbe:
            tcpSocket:
              port: 8080
```

Instead, only an `exec` probe that runs a shell command inside the container can be used that relies in this case on the presence of the `nc` command in the container image:

```
    readinessProbe:
      exec:
        command: ["nc", "-z", "-v", "-w5", "127.0.0.1", "8080"] 
```



x-pack/plugin/shutdown/qa/multi-node/src/javaRestTest/java/org/elasticsearch/xpack/shutdown/NodeShutdownIT.java
checkTypeChange("RESTART", "REMOVE");
    }
    public void testPutShutdownCanChangeTypeFromRemoveToRestart() throws Exception {
        checkTypeChange("REMOVE", "RESTART");
    }
    @SuppressWarnings("unchecked")
    public void checkTypeChange(String fromType, String toType) throws Exception {
        String nodeIdToShutdown = getRandomNodeId();
        String type = fromType;
        
        putNodeShutdown(nodeIdToShutdown, type);
        
        String newReason = "this reason is different";
        String newType = toType;
        
        Request putShutdown = new Request("PUT", "_nodes/" + nodeIdToShutdown + "/shutdown");
        putShutdown.setJsonEntity("{\"type\":  \"" + newType + "\", \"reason\":  \"" + newReason + "\"}");
        assertOK(client().performRequest(putShutdown));
        
        {
            Request getShutdownStatus = new Request("GET", "_nodes/" + nodeIdToShutdown + "/shutdown");
            Map<String, Object> statusResponse = responseAsMap(client().performRequest(getShutdownStatus));
            List<Map<String, Object>> nodesArray = (List<Map<String, Object>>) statusResponse.get("nodes");
            assertThat(nodesArray, hasSize(1));
            assertThat(nodesArray.get(0).get("node_id"), equalTo(nodeIdToShutdown));
            assertThat(nodesArray.get(0).get("type"), equalTo(newType));
            assertThat(nodesArray.get(0).get("reason"), equalTo(newReason));
        }
    }
    /**