### 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)

"""Duration calculation."""
        end_date = self.get("end_date")
        duration = self.get("duration")
        if end_date and duration:
            return td_format(datetime.timedelta(seconds=duration))
        return None
    formatters_columns = {
        "dag_id": wwwutils.dag_link,
        "task_id": wwwutils.task_instance_link,
        "start_date": wwwutils.datetime_f("start_date"),
        "end_date": wwwutils.datetime_f("end_date"),
        "dag_run.execution_date": wwwutils.datetime_f("dag_run.execution_date"),
        "reschedule_date": wwwutils.datetime_f("reschedule_date"),
        "duration": duration_f,
        "map_index": wwwutils.format_map_index,
    }
class TriggerModelView(AirflowModelView):