### 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)

)
        operator.execute(None)
        self.client_mock.create_container.assert_called_once_with(
            command="env",
            name="test_container",
            environment={
                "AIRFLOW_TMP_DIR": TEST_AIRFLOW_TEMP_DIRECTORY,
                "UNIT": "TEST",
                "PRIVATE": "MESSAGE",
                "ENV": "FILE",
                "VAR": "VALUE",
            },
            host_config=self.client_mock.create_host_config.return_value,
            image=TEST_IMAGE,
            user=None,
            entrypoint=["sh", "-c"],
            working_dir="/container/path",
            tty=True,
            hostname=TEST_CONTAINER_HOSTNAME,
        )
        self.client_mock.create_host_config.assert_called_once_with(
            mounts=[
                Mount(source="/host/path", target="/container/path", type="bind"),
                Mount(source="/mkdtemp", target=TEST_AIRFLOW_TEMP_DIRECTORY, type="bind"),
            ],
            network_mode="bridge",
            shm_size=1000,
            cpu_shares=1024,
            mem_limit=None,
            auto_remove=False,