### 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)

"start_date": (dag.start_date or now).date().isoformat(),
            "end_date": (dag.end_date or now).date().isoformat(),
        }
        return self.render_template(
            "airflow/calendar.html",
            dag=dag,
            doc_md=wwwutils.wrapped_markdown(getattr(dag, "doc_md", None)),
            data=htmlsafe_json_dumps(data, separators=(",", ":")),  
            root=root,
            dag_model=dag_model,
        )
    @expose("/graph")
    @auth.has_access(
        [
            (permissions.ACTION_CAN_READ, permissions.RESOURCE_DAG),
            (permissions.ACTION_CAN_READ, permissions.RESOURCE_TASK_INSTANCE),
            (permissions.ACTION_CAN_READ, permissions.RESOURCE_TASK_LOG),
        ]
    )
    @gzipped
    @action_logging
    def legacy_graph(self):
        """Redirect from url param."""
        return redirect(url_for("Airflow.graph", **sanitize_args(request.args)))
    @expose("/dags/<string:dag_id>/graph")
    @auth.has_access(
        [
            (permissions.ACTION_CAN_READ, permissions.RESOURCE_DAG),
            (permissions.ACTION_CAN_READ, permissions.RESOURCE_TASK_INSTANCE),
            (permissions.ACTION_CAN_READ, permissions.RESOURCE_TASK_LOG),