### 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)

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                    form_fields[k]["schema"]["type"] = ["object", "null"]
            
            if (
                "description_html" in form_fields[k]["schema"]
                and form_fields[k]["schema"]["description_html"]
            ):
                form_fields[k]["description"] = Markup(form_fields[k]["schema"]["description_html"])
            if "custom_html_form" in form_fields[k]["schema"]:
                form_fields[k]["schema"]["custom_html_form"] = Markup(
                    form_fields[k]["schema"]["custom_html_form"]
                )
        if not dag_orm:
            flash(f"Cannot find dag {dag_id}")
            return redirect(origin)
        if dag_orm.has_import_errors:
            flash(f"Cannot create dagruns because the dag {dag_id} has import errors", "error")
            return redirect(origin)
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            session.query(
                DagRun.conf, func.max(DagRun.run_id).label("run_id"), func.max(DagRun.execution_date)
            )
            .filter(
                DagRun.dag_id == dag_id,
                DagRun.run_type == DagRunType.MANUAL,
                DagRun.conf.isnot(None),
            )
            .group_by(DagRun.conf)
            .order_by(func.max(DagRun.execution_date).desc())
            .limit(5)