### 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)

scheduler_job = SchedulerJobRunner.most_recent_job()
        if scheduler_job:
            latest_scheduler_heartbeat = scheduler_job.latest_heartbeat.isoformat()
            if scheduler_job.is_alive():
                scheduler_status = HEALTHY
    except Exception:
        metadatabase_status = UNHEALTHY
    try:
        triggerer_job = TriggererJobRunner.most_recent_job()
        if triggerer_job:
            latest_triggerer_heartbeat = triggerer_job.latest_heartbeat.isoformat()
            if triggerer_job.is_alive():
                triggerer_status = HEALTHY
        else:
            triggerer_status = None
    except Exception:
        metadatabase_status = UNHEALTHY
    payload = {
        "metadatabase": {"status": metadatabase_status},
        "scheduler": {
            "status": scheduler_status,
            "latest_scheduler_heartbeat": latest_scheduler_heartbeat,
        },
        "triggerer": {
            "status": triggerer_status,
            "latest_triggerer_heartbeat": latest_triggerer_heartbeat,
        },
    }
    return health_schema.dump(payload)