### 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)

"""Multiple delete."""
        self.datamodel.delete_all(items)
        self.update_redirect()
        return redirect(self.get_redirect())
    @action(
        "mulduplicate",
        "Duplicate",
        "Are you sure you want to duplicate the selected connections?",
        single=False,
    )
    @provide_session
    @auth.has_access(
        [
            (permissions.ACTION_CAN_CREATE, permissions.RESOURCE_CONNECTION),
            (permissions.ACTION_CAN_READ, permissions.RESOURCE_CONNECTION),
        ]
    )
    def action_mulduplicate(self, connections, session: Session = NEW_SESSION):