### 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)

"""Return a list of dot-separated dictionary paths."""
    for key, value in input_dict.items():
        if isinstance(value, dict):
            for sub_key in get_key_paths(value):
                yield ".".join((key, sub_key))
        else:
            yield key
def get_value_from_path(key_path, content):
    """Return the value from a dictionary based on dot-separated path of keys."""
    elem = content
    for x in key_path.strip(".").split("."):
        try:
            x = int(x)
            elem = elem[x]
        except ValueError:
            elem = elem.get(x)
    return elem
def get_task_stats_from_query(qry):