### 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)

if conf.has_option("email", key):
                    path = conf.get_mandatory_value("email", key)
                    try:
                        with open(path) as f:
                            content = f.read()
                    except FileNotFoundError:
                        self.log.warning(f"Could not find email template file '{path!r}'. Using defaults...")
                    except OSError:
                        self.log.exception(f"Error while using email template '{path!r}'. Using defaults...")
                return render_template_to_string(jinja_env.from_string(content), jinja_context)
            subject = render("subject_template", default_subject)
            html_content = render("html_content_template", default_html_content)
            html_content_err = render("html_content_template", default_html_content_err)
        return subject, html_content, html_content_err
    def email_alert(self, exception, task: BaseOperator) -> None:
        """Send alert email with exception information."""
        subject, html_content, html_content_err = self.get_email_subject_content(exception, task=task)
        assert task.email
        try:
            send_email(task.email, subject, html_content)
        except Exception:
            send_email(task.email, subject, html_content_err)
    def set_duration(self) -> None:
        """Set TI duration"""
        if self.end_date and self.start_date:
            self.duration = (self.end_date - self.start_date).total_seconds()
        else:
            self.duration = None
        self.log.debug("Task Duration set to %s", self.duration)
    def _record_task_map_for_downstreams(self, task: Operator, value: Any, *, session: Session) -> None: