### 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)

x_axis_date=True,
            x_axis_format=LINECHART_X_AXIS_TICKFORMAT,
            height=chart_height,
            chart_attr=self.line_chart_attr,
        )
        tis = dag.get_task_instances_before(base_date, num_runs, session=session)
        for task in dag.tasks:
            y_points = []
            x_points = []
            for ti in tis:
                if ti.task_id != task.task_id:
                    continue
                dttm = wwwutils.epoch(ti.execution_date)
                x_points.append(dttm)
                
                y_points.append(ti.prev_attempted_tries)
            if x_points:
                chart.add_serie(name=task.task_id, x=x_points, y=y_points)
        tries = sorted({ti.try_number for ti in tis})
        max_date = max(ti.execution_date for ti in tis) if tries else None
        chart.create_y_axis("yAxis", format=".02f", custom_format=False, label="Tries")
        chart.axislist["yAxis"]["axisLabelDistance"] = "-15"
        session.commit()
        form = DateTimeWithNumRunsForm(
            data={
                "base_date": max_date or timezone.utcnow(),
                "num_runs": num_runs,
            }
        )
        chart.buildcontent()