### 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)

"""View to show records from Variable table."""
    route_base = "/variable"
    list_template = "airflow/variable_list.html"
    edit_template = "airflow/variable_edit.html"
    show_template = "airflow/variable_show.html"
    show_widget = AirflowVariableShowWidget
    datamodel = AirflowModelView.CustomSQLAInterface(models.Variable)  
    class_permission_name = permissions.RESOURCE_VARIABLE
    method_permission_name = {
        "add": "create",
        "list": "read",
        "edit": "edit",
        "show": "read",
        "delete": "delete",
        "action_muldelete": "delete",