### 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
Map<String, Object> httpObject = (Map<String, Object>) nodeObject.get("http");
        String publishAddress = (String) httpObject.get("publish_address");
        String readinessPorts = this.getTestReadinessPorts();
        String restPorts = this.getTestRestCluster();
        String[] restAddresses = restPorts.split(",");
        int nodeIndex = 0;
        for (String restAddress : restAddresses) {
            
            if (restAddress.startsWith("[")) {
                continue;
            }
            if (restAddress.equals(publishAddress)) {
                break;
            }
            nodeIndex++;
        }
        String[] readinessAddresses = readinessPorts.split(",");
        String readinessAddress = readinessAddresses[nodeIndex];
        String portStr = readinessAddress.split(":")[1];
        Integer port = Integer.parseInt(portStr);
        
        tcpReadinessProbeTrue(port);
        
        checkCRUD(nodeId, randomFrom("restart", "RESTART"), "1ms", null, false);
        tcpReadinessProbeFalse(port);
        
        Request deleteRequest = new Request("DELETE", "_nodes/" + nodeId + "/shutdown");
        assertOK(client().performRequest(deleteRequest));
        assertNoShuttingDownNodes(nodeId);
        tcpReadinessProbeTrue(port);