### 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:
            if self.state == State.QUEUED:
                
                self._try_number += 1
            self.state = State.UP_FOR_RETRY
            email_for_state = operator.attrgetter("email_on_retry")
            callbacks = task.on_retry_callback if task else None
            callback_type = "on_retry"
        self._log_state("Immediate failure requested. " if force_fail else "")
        if task and email_for_state(task) and task.email:
            try:
                self.email_alert(error, task)
            except Exception:
                self.log.exception("Failed to send email to: %s", task.email)
        if callbacks and context:
            self._run_finished_callback(callbacks, context, callback_type)
        if not test_mode:
            session.merge(self)
            session.flush()
    def is_eligible_to_retry(self):
        """Is task instance is eligible for retry"""
        if self.state == State.RESTARTING:
            
            
            return True
        if not getattr(self, "task", None):
            
            return self.try_number <= self.max_tries
        return self.task.retries and self.try_number <= self.max_tries
    def get_template_context(