### 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)

table = [
                (section, key, str(value), source)
                for section, parameters in conf.as_dict(True, display_sensitive).items()
                for key, (value, source) in parameters.items()
            ]
            return self.render_template(
                template="airflow/config.html",
                title=title,
                table=table,
            )
        else:
            return self.render_template(
                "airflow/config.html",
                title=title,
                hide_config_msg=(
                    "Your Airflow administrator chose not to expose the configuration, "
                    "most likely for security reasons."
                ),
            )
class RedocView(AirflowBaseView):
    """Redoc Open API documentation."""
    default_view = "redoc"
    @expose("/redoc")
    def redoc(self):
        """Redoc API documentation."""
        openapi_spec_url = url_for("/api/v1./api/v1_openapi_yaml")
        return self.render_template("airflow/redoc.html", openapi_spec_url=openapi_spec_url)
class DagFilter(BaseFilter):
    """Filter using DagIDs."""
    def apply(self, query, func):