### 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)

if dt is None:
                        break
                    if dt.year != year:
                        break
                    if dag.end_date and dt > dag.end_date:
                        break
                    dates[dt.date()] += 1
            else:
                prev_logical_date = DateTime.min
                while True:
                    curr_info = dag.timetable.next_dagrun_info(
                        last_automated_data_interval=last_automated_data_interval,
                        restriction=restriction,
                    )
                    if curr_info is None:
                        break  
                    if curr_info.logical_date <= prev_logical_date:
                        break  
                    if curr_info.logical_date.year != year:
                        break  
                    last_automated_data_interval = curr_info.data_interval
                    dates[curr_info.logical_date] += 1
                    prev_logical_date = curr_info.logical_date
            data_dag_states.extend(
                {"date": date.isoformat(), "state": "planned", "count": count}
                for (date, count) in dates.items()
            )
        now = DateTime.utcnow()
        data = {
            "dag_states": data_dag_states,