### 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)

def mutate_task_instance(task_instance):
            if task_instance.queue == "queue1":
                task_instance.queue = "queue2"
            else:
                task_instance.queue = "queue1"
        mock_hook.side_effect = mutate_task_instance
        dag = DAG("test_task_instance_mutation_hook", start_date=DEFAULT_DATE)
        dag.add_task(EmptyOperator(task_id="task_to_mutate", owner="test", queue="queue1"))
        dagrun = self.create_dag_run(dag, session=session)
        task = dagrun.get_task_instances()[0]
        task.state = state
        session.merge(task)
        session.commit()
        assert task.queue == "queue2"
        dagrun.verify_integrity()
        task = dagrun.get_task_instances()[0]
        assert task.queue == "queue1"
    @pytest.mark.parametrize(
        "prev_ti_state, is_ti_success",
        [
            (TaskInstanceState.SUCCESS, True),
            (TaskInstanceState.SKIPPED, True),
            (TaskInstanceState.RUNNING, False),
            (TaskInstanceState.FAILED, False),
            (None, False),
        ],
    )
    def test_depends_on_past(self, session, prev_ti_state, is_ti_success):