### 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)

TEST_HOST_TEMP_DIRECTORY = "/tmp/host/dir"
TEST_AIRFLOW_TEMP_DIRECTORY = "/tmp/airflow/dir"
TEST_ENTRYPOINT = '["sh", "-c"]'
TEMPDIR_MOCK_RETURN_VALUE = "/mkdtemp"
@pytest.mark.parametrize("docker_conn_id", [pytest.param(None, id="empty-conn-id"), TEST_CONN_ID])
@pytest.mark.parametrize(
    "tls_params",
    [
        pytest.param({}, id="empty-tls-params"),
        pytest.param(
            {
                "tls_ca_cert": "foo",
                "tls_client_cert": "bar",
                "tls_client_key": "spam",
                "tls_hostname": "egg",
                "tls_ssl_version": "super-secure",
            },
            id="all-tls-params",
        ),
    ],
)
def test_hook_usage(docker_hook_patcher, docker_conn_id, tls_params: dict):
    """Test that operator use DockerHook."""
    docker_hook_patcher.construct_tls_config.return_value = "MOCK-TLS-VALUE"
    expected_tls_call_args = {
        "ca_cert": tls_params.get("tls_ca_cert"),
        "client_cert": tls_params.get("tls_client_cert"),
        "client_key": tls_params.get("tls_client_key"),
        "assert_hostname": tls_params.get("tls_hostname"),
        "ssl_version": tls_params.get("tls_ssl_version"),