### 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)

dags_query = dags_query.where(DagModel.dag_id.in_(filter_dag_ids))
            filtered_dag_count = get_query_count(dags_query, session=session)
            if filtered_dag_count == 0 and len(arg_tags_filter):
                flash(
                    "No matching DAG tags found.",
                    "warning",
                )
                flask_session[FILTER_TAGS_COOKIE] = None
                return redirect(url_for("Airflow.index"))
            all_dags = dags_query
            active_dags = dags_query.where(~DagModel.is_paused)
            paused_dags = dags_query.where(DagModel.is_paused)
            
            running_dags = dags_query.join(DagRun, DagModel.dag_id == DagRun.dag_id).where(
                DagRun.state == DagRunState.RUNNING
            )
            
            subq_all = (
                select(DagRun.dag_id, func.max(DagRun.start_date).label("start_date"))
                .group_by(DagRun.dag_id)
                .subquery()
            )
            subq_failed = (
                select(DagRun.dag_id, func.max(DagRun.start_date).label("start_date"))
                .where(DagRun.state == DagRunState.FAILED)
                .group_by(DagRun.dag_id)
                .subquery()
            )
            subq_join = (
                select(subq_all.c.dag_id, subq_all.c.start_date)