### 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)

"""Duplicate Multiple connections."""
        for selected_conn in connections:
            new_conn_id = selected_conn.conn_id
            match = re2.search(r"_copy(\d+)$", selected_conn.conn_id)
            base_conn_id = selected_conn.conn_id
            if match:
                base_conn_id = base_conn_id.split("_copy")[0]
            potential_connection_ids = [f"{base_conn_id}_copy{i}" for i in range(1, 11)]
            query = session.scalars(
                select(Connection.conn_id).where(Connection.conn_id.in_(potential_connection_ids))
            )
            found_conn_id_set = {conn_id for conn_id in query}
            possible_conn_id_iter = (
                connection_id
                for connection_id in potential_connection_ids
                if connection_id not in found_conn_id_set
            )
            try:
                new_conn_id = next(possible_conn_id_iter)
            except StopIteration:
                flash(