### 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)

child_instances = [
                    item
                    for sublist in (child["instances"] for child in children if "instances" in child)
                    for item in sublist
                    if item and item["run_id"] == run_id
                ]
                children_queued_dttms = (item["queued_dttm"] for item in child_instances)
                children_start_dates = (item["start_date"] for item in child_instances)
                children_end_dates = (item["end_date"] for item in child_instances)
                children_states = {item["state"] for item in child_instances}
                
                
                
                mapped_states: MutableMapping[str, int] = collections.defaultdict(int)
                for mis in mapped_instances.values():
                    child_states = {mi.state for mi in mis}
                    state = next(s for s in wwwutils.priority if s in child_states)
                    value = state.value if state is not None else "no_status"
                    mapped_states[value] += 1