### 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)

hosts_obj = mock.Mock()
        operator = DockerOperator(task_id="test", image="test", extra_hosts=hosts_obj)
        operator.execute(None)
        self.client_mock.create_container.assert_called_once()
        assert "host_config" in self.client_mock.create_container.call_args[1]
        assert "extra_hosts" in self.client_mock.create_host_config.call_args[1]
        assert hosts_obj is self.client_mock.create_host_config.call_args[1]["extra_hosts"]
    def test_privileged(self):
        privileged = mock.Mock()
        operator = DockerOperator(task_id="test", image="test", privileged=privileged)
        operator.execute(None)
        self.client_mock.create_container.assert_called_once()
        assert "host_config" in self.client_mock.create_container.call_args[1]
        assert "privileged" in self.client_mock.create_host_config.call_args[1]
        assert privileged is self.client_mock.create_host_config.call_args[1]["privileged"]