### 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)

"""Get Dag's grid view."""
        dag = get_airflow_app().dag_bag.get_dag(dag_id, session=session)
        dag_model = DagModel.get_dagmodel(dag_id, session=session)
        if not dag:
            flash(f'DAG "{dag_id}" seems to be missing from DagBag.', "error")
            return redirect(url_for("Airflow.index"))
        wwwutils.check_import_errors(dag.fileloc, session)
        wwwutils.check_dag_warnings(dag.dag_id, session)
        root = request.args.get("root")
        if root:
            dag = dag.partial_subset(task_ids_or_regex=root, include_downstream=False, include_upstream=True)
        num_runs = request.args.get("num_runs", type=int)
        if num_runs is None:
            num_runs = conf.getint("webserver", "default_dag_run_display_number")
        doc_md = wwwutils.wrapped_markdown(getattr(dag, "doc_md", None))
        task_log_reader = TaskLogReader()
        if task_log_reader.supports_external_link:
            external_log_name = task_log_reader.log_handler.log_name
        else:
            external_log_name = None
        default_dag_run_display_number = conf.getint("webserver", "default_dag_run_display_number")
        num_runs_options = [5, 25, 50, 100, 365]
        if default_dag_run_display_number not in num_runs_options:
            insort_left(num_runs_options, default_dag_run_display_number)
        return self.render_template(