### 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)

"""Clears the DagRun."""
        dag_id = request.form.get("dag_id")
        dag_run_id = request.form.get("dag_run_id")
        confirmed = request.form.get("confirmed") == "true"
        dag = get_airflow_app().dag_bag.get_dag(dag_id)
        dr = dag.get_dagrun(run_id=dag_run_id)
        start_date = dr.logical_date
        end_date = dr.logical_date
        return self._clear_dag_tis(
            dag,
            start_date,
            end_date,
            origin=None,
            recursive=True,
            confirmed=confirmed,
            session=session,
        )
    @expose("/blocked", methods=["POST"])
    @auth.has_access(
        [
            (permissions.ACTION_CAN_EDIT, permissions.RESOURCE_DAG),
            (permissions.ACTION_CAN_READ, permissions.RESOURCE_DAG_RUN),
        ]
    )
    @provide_session
    def blocked(self, session: Session = NEW_SESSION):