### 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)

f"Given execution date, {execution_date}, could not be identified as a date. "
                "Example date format: 2015-11-16T14:34:15+00:00"
            )
            return {"error": error_message}, 400
        task_log_reader = TaskLogReader()
        if not task_log_reader.supports_read:
            return {
                "message": "Task log handler does not support read logs.",
                "error": True,
                "metadata": {"end_of_log": True},
            }
        ti = session.scalar(
            select(models.TaskInstance)
            .where(
                TaskInstance.task_id == task_id,
                TaskInstance.dag_id == dag_id,
                TaskInstance.execution_date == execution_date,
                TaskInstance.map_index == map_index,
            )
            .join(TaskInstance.dag_run)
            .options(joinedload(TaskInstance.trigger).joinedload(Trigger.triggerer_job))
            .limit(1)
        )
        if ti is None:
            return {
                "message": "*** Task instance did not exist in the DB\n",
                "error": True,
                "metadata": {"end_of_log": True},
            }
        try: