### 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)

(permissions.ACTION_CAN_READ, permissions.RESOURCE_DAG_RUN),
        ]
    )
    @provide_session
    def last_dagruns(self, session: Session = NEW_SESSION):
        """Last DAG runs."""
        allowed_dag_ids = get_airflow_app().appbuilder.sm.get_accessible_dag_ids(g.user)
        
        selected_dag_ids = {unquote(dag_id) for dag_id in request.form.getlist("dag_ids") if dag_id}
        if selected_dag_ids:
            filter_dag_ids = selected_dag_ids.intersection(allowed_dag_ids)
        else:
            filter_dag_ids = allowed_dag_ids
        if not filter_dag_ids:
            return flask.json.jsonify({})
        last_runs_subquery = (
            session.query(
                DagRun.dag_id,
                sqla.func.max(DagRun.execution_date).label("max_execution_date"),
            )
            .group_by(DagRun.dag_id)
            .filter(DagRun.dag_id.in_(filter_dag_ids))  
            .subquery("last_runs")
        )
        query = session.query(
            DagRun.dag_id,
            DagRun.start_date,
            DagRun.end_date,
            DagRun.state,
            DagRun.execution_date,