### Apache Airflow version

main (development)

### What happened

https://github.com/apache/airflow/pull/27755 added the triggerer to the rest api health endpoint, but not the main one served on `/health`.

### What you think should happen instead

As documented [here](https://airflow.apache.org/docs/apache-airflow/2.6.1/administration-and-deployment/logging-monitoring/check-health.html#webserver-health-check-endpoint), the `/health` endpoint should include triggerer info like shown on `/api/v1/health`.

### How to reproduce

Compare `/api/v1/health` and `/health` responses.

### Operating System

mac os

### Versions of Apache Airflow Providers

_No response_

### Deployment

Virtualenv installation

### 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)

}
            return [get_mapped_group_summary(run_id, tis) for run_id, tis in mapped_tis.items()]
        
        if task_group.group_id is None:
            return {
                "id": task_group.group_id,
                "label": task_group.label,
                "children": children,
                "instances": [],
            }
        if group_is_mapped:
            mapped_group_summaries = get_mapped_group_summaries()
            return {
                "id": task_group.group_id,
                "label": task_group.label,
                "children": children,
                "tooltip": task_group.tooltip,
                "instances": mapped_group_summaries,
                "is_mapped": group_is_mapped,
            }
        group_summaries = [get_summary(dr) for dr in dag_runs]
        return {
            "id": task_group.group_id,
            "label": task_group.label,
            "children": children,
            "tooltip": task_group.tooltip,
            "instances": group_summaries,
        }
    return task_group_to_grid(dag.task_group, grouped_tis, is_parent_mapped=False)
def get_key_paths(input_dict):