When you write mount_path=shared_data_mount_path, you're literally passing the parameter object itself, not its value. Airflow sees this and goes "what the hell?" and can't serialize it.

Working solution

Just use regular Airflow templates:

@dag(
    dag_id=PIPELINE_NAME,
    schedule=None,
    params={
        "command": "",
        "image": "python:3.13-slim", 
        "shared_data_mount_path": "/mnt/data/"
    }
)
def run_arbitary_command_pipeline():
    # your code...
    
    run_command = KubernetesPodOperator(
        task_id="run_arbitrary_command",
        cmds=["sh", "-c", "{{ params.command }}"],
        image="{{ params.image }}",
        volume_mounts=[k8s.V1VolumeMount(
            name=pvc_name, 
            mount_path="{{ params.shared_data_mount_path }}"  # this works
        )],
        # rest of your stuff...
    )

What was wrong

Your first attempt didn't work because you were passing the actual parameter object, not a template string. Airflow only knows how to process strings like "{{ params.something }}".

Your second attempt with explicit "{{ params.shared_data_mount_path }}" should have worked. If it didn't, maybe there was a typo somewhere or the parameter wasn't properly defined in params.

Try the solution above - should work without issues.