### 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)

#
#
from __future__ import annotations
from airflow.api_connexion.schemas.health_schema import health_schema
from airflow.api_connexion.types import APIResponse
from airflow.jobs.scheduler_job_runner import SchedulerJobRunner
from airflow.jobs.triggerer_job_runner import TriggererJobRunner
HEALTHY = "healthy"
UNHEALTHY = "unhealthy"
def get_health() -> APIResponse:
    """Return the health of the airflow scheduler and metadatabase."""
    metadatabase_status = HEALTHY
    latest_scheduler_heartbeat = None
    latest_triggerer_heartbeat = None
    scheduler_status = UNHEALTHY
    triggerer_status: str | None = UNHEALTHY
    try: