### 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)

A positive integer plus a modifier representing the unit of measure (k, m, or g).
        Eg: 10m or 1g Defaults to -1 (unlimited).
    :param log_opts_max_file: The maximum number of log files that can be present.
        If rolling the logs creates excess files, the oldest file is removed.
        Only effective when max-size is also set. A positive integer. Defaults to 1.
    :param ipc_mode: Set the IPC mode for the container.
    """
    template_fields: Sequence[str] = ("image", "command", "environment", "env_file", "container_name")
    template_fields_renderers = {"env_file": "yaml"}
    template_ext: Sequence[str] = (
        ".sh",
        ".bash",
        ".env",
    )
    def __init__(
        self,
        *,
        image: str,
        api_version: str | None = None,
        command: str | list[str] | None = None,
        container_name: str | None = None,
        cpus: float = 1.0,
        docker_url: str = "unix://var/run/docker.sock",
        environment: dict | None = None,
        private_environment: dict | None = None,
        env_file: str | None = None,
        force_pull: bool = False,
        mem_limit: float | str | None = None,
        host_tmp_dir: str | None = None,
        network_mode: str | None = None,