### Apache Airflow version

2.7.0rc2

### What happened

In the Airflow UI, currently, the DAG Processor is visible in the Cluster Activity page even if there is no stand-alone dag processor. 

### What you think should happen instead

It should be hidden if there is no stand-alone dag processor.

### How to reproduce

Run Airflow 2.7 

### Operating System

Mac OS

### Versions of Apache Airflow Providers

Airflow > 2.7

### Deployment

Official Apache Airflow Helm Chart

### Deployment details

_No response_

### Anything else

_No response_

### Are you willing to submit PR?

- [X] 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)

select(TaskInstance.state, sqla.func.count(TaskInstance.dag_id))
            .where(TaskInstance.dag_id == dag_id)
            .group_by(TaskInstance.state)
        ).all()
        active_runs = models.DagRun.find(dag_id=dag_id, state=DagRunState.RUNNING, external_trigger=False)
        tags = session.scalars(select(models.DagTag).where(models.DagTag.dag_id == dag_id)).all()
        
        owner_links = session.execute(select(DagOwnerAttributes).filter_by(dag_id=dag_id)).all()
        attrs_to_avoid = [
            "schedule_datasets",
            "schedule_dataset_references",
            "task_outlet_dataset_references",
            "NUM_DAGS_PER_DAGRUN_QUERY",
            "serialized_dag",
            "tags",
            "default_view",
            "relative_fileloc",
            "dag_id",
            "description",
            "max_active_runs",
            "max_active_tasks",
            "schedule_interval",
            "owners",
            "dag_owner_links",
            "is_paused",
        ]
        attrs_to_avoid.extend(wwwutils.get_attr_renderer().keys())
        dag_model_attrs: list[tuple[str, Any]] = [
            (attr_name, attr)
            for attr_name, attr in (