Trigger Gitlab pipeline with own TRIGGER_PAYLOAD data using python-gitlab?

Question

I am trying to trigger our Gitlab pipeline with following content of TRIGGER_PAYLOAD variable using python-gitlab library:

trigger_payload = {
    "project": {
        "id": project_id,
        "http_url": http_url,
        "web_url": web_url,
        "namespace": repo_namespace,
        "path_with_namespace": path_with_namespace
    },
    "checkout_sha": commit_id,
    "event_name": "tag_push"
}

# Convert the payload to a JSON string
trigger_payload_str = json.dumps(trigger_payload)

# Create a GitLab API instance
gl = gitlab.Gitlab(gitlab_url, private_token=gitlab_token)

# Get the project
project = gl.projects.get(project_id)

# Trigger the pipeline and pass the JSON payload
pipeline = project.trigger_pipeline(ref=ref, variables={'TRIGGER_PAYLOAD': trigger_payload_str})

Problem is, that TRIGGER_PAYLOAD variable is already set (as one of the default variables in GitLab) and can't be changed. I aways receive an error:

gitlab.exceptions.GitlabCreateError: 422: {'base': ['Duplicate variable name: TRIGGER_PAYLOAD']}

But when I choose different variable name, pipeline fails, because it's expecting above mentioned data structure.

How to fix it?