### 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)

else:
            ti = qry.one_or_none()
        if ti:
            
            self.start_date = ti.start_date
            self.end_date = ti.end_date
            self.duration = ti.duration
            self.state = ti.state
            
            self.try_number = ti.try_number
            self.max_tries = ti.max_tries
            self.hostname = ti.hostname
            self.unixname = ti.unixname
            self.job_id = ti.job_id
            self.pool = ti.pool
            self.pool_slots = ti.pool_slots or 1
            self.queue = ti.queue
            self.priority_weight = ti.priority_weight
            self.operator = ti.operator
            self.queued_dttm = ti.queued_dttm
            self.queued_by_job_id = ti.queued_by_job_id
            self.pid = ti.pid
            self.executor_config = ti.executor_config
            self.external_executor_id = ti.external_executor_id
            self.trigger_id = ti.trigger_id
            self.next_method = ti.next_method
            self.next_kwargs = ti.next_kwargs
        else:
            self.state = None
    def refresh_from_task(self, task: Operator, pool_override: str | None = None) -> None: