### Apache Airflow version

2.5.0

### What happened

Kubernetes pod operator failed to push xcom value.

After upgrading airflow from 2.2.4 to 2.5.0 (and apache-airflow-providers-cncf-kubernetes from 3.0.2 to 5.0.0) pushing of xcom values from kubernetes pod operator stopped working.



### What you think should happen instead

Example of log before the upgrade
```
[2023-01-17 06:57:54,357] {pod_launcher.py:313} INFO - Running command... cat /airflow/xcom/return.json

[2023-01-17 06:57:54,398] {pod_launcher.py:313} INFO - Running command... kill -s SIGINT 1

[2023-01-17 06:57:55,012] {pod_launcher.py:186} INFO - ["No non-accuracy metrics changed more than 10.0% between 2023-01-15 and 2023-01-16\n"]
```
and after the upgrade
```
[2023-01-18T07:12:32.784+0900] {pod_manager.py:368} INFO - Checking if xcom sidecar container is started.
[2023-01-18T07:12:32.804+0900] {pod_manager.py:372} INFO - The xcom sidecar container is started.
[2023-01-18T07:12:32.845+0900] {pod_manager.py:407} INFO - Running command... if [ -s /airflow/xcom/return.json ]; then cat /airflow/xcom/return.json; else echo __airflow_xcom_result_empty__; fi

[2023-01-18T07:12:32.895+0900] {pod_manager.py:407} INFO - Running command... kill -s SIGINT 1

[2023-01-18T07:12:33.405+0900] {kubernetes_pod.py:431} INFO - Result file is empty.
```


Looking at other timestamps in the log file, it appears that the xcom sidecar is run before the pod finishes, instead of waiting until the end.

### How to reproduce

I used `airflow.providers.cncf.kubernetes.operators.kubernetes_pod.KubernetesPodOperator` with `get_logs=False`.

### Operating System

Debian GNU/Linux 11 (bullseye) (based on official airflow image)

### Versions of Apache Airflow Providers

apache-airflow-providers-cncf-kubernetes 3.0.2 and 5.0.0

### Deployment

Official Apache Airflow Helm Chart

### Deployment details

Deployed on GKE using the official helm chart

### Anything else

_No response_

### Are you willing to submit PR?

- [ ] Yes I am willing to submit a PR!

### Code of Conduct

- [X] I agree to follow this project's [Code of Conduct](https://github.com/apache/airflow/blob/main/CODE_OF_CONDUCT.md)

"""
    Helper class for creating, monitoring, and otherwise interacting with Kubernetes pods
    for use with the KubernetesPodOperator
    """
    def __init__(
        self,
        kube_client: client.CoreV1Api = None,
        in_cluster: bool = True,
        cluster_context: str | None = None,
    ):
        """
        Creates the launcher.
        :param kube_client: kubernetes client
        :param in_cluster: whether we are in cluster
        :param cluster_context: context of the cluster
        """
        super().__init__()
        if kube_client:
            self._client = kube_client
        else:
            self._client = get_kube_client(in_cluster=in_cluster, cluster_context=cluster_context)
            warnings.warn(
                "`kube_client` not supplied to PodManager. "
                "This will be a required argument in a future release. "
                "Please use KubernetesHook to create the client before calling.",
                DeprecationWarning,
            )
        self._watch = watch.Watch()
    def run_pod_async(self, pod: V1Pod, **kwargs) -> V1Pod: