### 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)

env_file_vars = self.unpack_environment_variables(self.env_file)
        self.container = self.cli.create_container(
            command=self.format_command(self.command),
            name=self.container_name,
            environment={**env_file_vars, **self.environment, **self._private_environment},
            host_config=self.cli.create_host_config(
                auto_remove=False,
                mounts=target_mounts,
                network_mode=self.network_mode,
                shm_size=self.shm_size,
                dns=self.dns,
                dns_search=self.dns_search,
                cpu_shares=int(round(self.cpus * 1024)),
                mem_limit=self.mem_limit,
                cap_add=self.cap_add,
                extra_hosts=self.extra_hosts,
                privileged=self.privileged,
                device_requests=self.device_requests,
                log_config=LogConfig(config=docker_log_config),
                ipc_mode=self.ipc_mode,
            ),
            image=self.image,
            user=self.user,
            entrypoint=self.format_command(self.entrypoint),
            working_dir=self.working_dir,
            tty=self.tty,
            hostname=self.hostname,
        )
        logstream = self.cli.attach(container=self.container["Id"], stdout=True, stderr=True, stream=True)
        try: