### Apache Airflow version

Other Airflow 2 version (please specify below)

### What happened

Airflow 2.3.3

Raising the `AirflowSkipException` in the source code, using the `DockerOperator`, is supposed to mark the task as skipped, according to the [docs](https://airflow.apache.org/docs/apache-airflow/stable/concepts/tasks.html#special-exceptions). However, what happens is that the task is marked as failed with the logs showing `ERROR - Task failed with exception`.

### What you think should happen instead

Tasks should be marked as skipped, not failed.

### How to reproduce

Raise the `AirflowSkipException` in the python source code, while using the `DockerOperator`.

### Operating System

Ubuntu 20.04.5 LTS (GNU/Linux 5.4.0-125-generic x86_64)

### Versions of Apache Airflow Providers

_No response_

### Deployment

Docker-Compose

### Deployment details

_No response_

### 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)

self.network_mode = network_mode
        self.tls_ca_cert = tls_ca_cert
        self.tls_client_cert = tls_client_cert
        self.tls_client_key = tls_client_key
        self.tls_hostname = tls_hostname
        self.tls_ssl_version = tls_ssl_version
        self.mount_tmp_dir = mount_tmp_dir
        self.tmp_dir = tmp_dir
        self.user = user
        self.mounts = mounts or []
        self.entrypoint = entrypoint
        self.working_dir = working_dir
        self.xcom_all = xcom_all
        self.docker_conn_id = docker_conn_id
        self.shm_size = shm_size
        self.tty = tty
        self.hostname = hostname
        self.privileged = privileged
        self.cap_add = cap_add
        self.extra_hosts = extra_hosts
        self.container: dict = None  
        self.retrieve_output = retrieve_output
        self.retrieve_output_path = retrieve_output_path
        self.timeout = timeout
        self.device_requests = device_requests
        self.log_opts_max_size = log_opts_max_size
        self.log_opts_max_file = log_opts_max_file
        self.ipc_mode = ipc_mode
    @cached_property
    def hook(self) -> DockerHook: