### 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)

"""Display DAG dependencies."""
        title = "DAG Dependencies"
        if not self.nodes or not self.edges:
            self._calculate_graph()
            self.last_refresh = timezone.utcnow()
        elif timezone.utcnow() > self.last_refresh + self.refresh_interval:
            max_last_updated = SerializedDagModel.get_max_last_updated_datetime()
            if max_last_updated is None or max_last_updated > self.last_refresh:
                self._calculate_graph()
            self.last_refresh = timezone.utcnow()
        return self.render_template(
            "airflow/dag_dependencies.html",
            title=title,
            nodes=self.nodes,
            edges=self.edges,
            last_refresh=self.last_refresh,
            arrange=conf.get("webserver", "dag_orientation"),
            width=request.args.get("width", "100%"),
            height=request.args.get("height", "800"),
        )
    def _calculate_graph(self):