### 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)

if add_tmp_variable:
            self.environment["AIRFLOW_TMP_DIR"] = self.tmp_dir
        else:
            self.environment.pop("AIRFLOW_TMP_DIR", None)
        docker_log_config = {}
        if self.log_opts_max_size is not None:
            docker_log_config["max-size"] = self.log_opts_max_size
        if self.log_opts_max_file is not None:
            docker_log_config["max-file"] = self.log_opts_max_file
        env_file_vars = {}
        if self.env_file is not None: