### 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)

session.add(TaskFail(ti=self))
        self.clear_next_method_args()
        
        if context is None and getattr(self, "task", None):
            context = self.get_template_context(session)
        if context is not None:
            context["exception"] = error
        
        
        
        
        
        
        
        
        
        task: BaseOperator | None = None
        try:
            if getattr(self, "task", None) and context:
                task = self.task.unmap((context, session))
        except Exception:
            self.log.error("Unable to unmap task to determine if we need to send an alert email")
        if force_fail or not self.is_eligible_to_retry():
            self.state = State.FAILED
            email_for_state = operator.attrgetter("email_on_failure")
            callbacks = task.on_failure_callback if task else None
            callback_type = "on_failure"
            if task and task.dag and task.dag.fail_stop:
                tis = self.get_dagrun(session).get_task_instances()
                stop_all_tasks_in_dag(tis, session, self.task_id)