### Apache Airflow version

2.5.1

### What happened

DagRun state and start_date are reset if somebody is clearing a task of the running DagRun.

### What you think should happen instead

I think we should not reset DagRun `state` and `start_date` in it's in the running or queued states because it doesn't make any sense for me. `state` and `start_date` of the DgRun should remain the same in case somebody's clearing a task of the running DagRun

### How to reproduce

Let's say we have a Dag with 2 tasks in it - short one and the long one:
```
dag = DAG(
    'dummy-dag',
    schedule_interval='@once',
    catchup=False,
)

DagContext.push_context_managed_dag(dag)

bash_success = BashOperator(
    task_id='bash-success',
    bash_command='echo "Start and finish"; exit 0',
    retries=0,
)

date_ind_success = BashOperator(
    task_id='bash-long-success',
    bash_command='echo "Start and finish"; sleep 300; exit 0',
)
```

Let's day we have a running Dagrun of this DAG. First task finishes in a second and the long one is still running. We have a start_date and duration set and the Dagrun is still running. It runs for example for a 30 secs (pic 1 and 2)

<img width="486" alt="image" src="https://user-images.githubusercontent.com/23456894/225335210-c2223ad1-771b-459d-b8ed-8f0aacb9b890.png">
<img width="492" alt="image" src="https://user-images.githubusercontent.com/23456894/225335272-ad737aef-2051-4e27-ae36-38c76d720c95.png">

Then we are clearing the short task. It causes clear of the Dagrun state (to `queued`) and clears `start_date` like we have a new Dagrun (pic 3 and 4)
<img width="407" alt="image" src="https://user-images.githubusercontent.com/23456894/225335397-6c7e0df7-a26a-46ed-8eaa-56ff928fc01a.png">
<img width="498" alt="image" src="https://user-images.githubusercontent.com/23456894/225335491-4d6a860a-e923-4878-b212-a6ccb4b590a3.png">

### Operating System

Unix/MacOS

### Versions of Apache Airflow Providers

_No response_

### 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)

"""
        Tests that dag scheduling delay stat is set properly once running scheduled dag.
        dag_run.update_state() invokes the _emit_true_scheduling_delay_stats_for_finished_state method.
        """
        dag = DAG(dag_id="test_emit_dag_stats", start_date=DEFAULT_DATE, schedule=schedule_interval)
        dag_task = EmptyOperator(task_id="dummy", dag=dag, owner="airflow")
        expected_stat_tags = {"dag_id": f"{dag.dag_id}", "run_type": DagRunType.SCHEDULED}
        try:
            info = dag.next_dagrun_info(None)
            orm_dag_kwargs = {"dag_id": dag.dag_id, "has_task_concurrency_limits": False, "is_active": True}
            if info is not None:
                orm_dag_kwargs.update(
                    {
                        "next_dagrun": info.logical_date,
                        "next_dagrun_data_interval": info.data_interval,
                        "next_dagrun_create_after": info.run_after,
                    },
                )
            orm_dag = DagModel(**orm_dag_kwargs)
            session.add(orm_dag)
            session.flush()
            dag_run = dag.create_dagrun(
                run_type=DagRunType.SCHEDULED,
                state=DagRunState.SUCCESS,
                execution_date=dag.start_date,
                data_interval=dag.infer_automated_data_interval(dag.start_date),
                start_date=dag.start_date,