### Apache Airflow version

2.7.0

Also reproduced on 2.5.0

### What happened

Recently we added some automation to restarting Airflow tasks with "clear" command so we use this feature a lot. We often clear tasks in RUNNING state, which means that they go into RESTARTING state. We noticed that a lot of those tasks get stuck in RESTARTING state. Our Airflow infrastructure runs in an environment where any process can get suddenly killed without graceful shutdown.

We run Airflow on GKE but I managed to reproduce this behaviour on local environment with SequentialExecutor. See **"How to reproduce"** below for details.

### What you think should happen instead

Tasks should get cleaned after scheduler restart and eventually get scheduled and executed.

### How to reproduce

After some code investigation, I reproduced this kind of behaviour on local environment and it seems that RESTARTING tasks are only properly handled if the original restarting task is gracefully shut down so it can mark task as UP_FOR_RETRY or at least there is a healthy scheduler to do it if they fail for any other reason. The problem is with the following scenario:

1. Task is initially in RUNNING state.
2. Scheduler process dies suddenly.
3. The task process also dies suddenly.
4. "clear" command is executed on the task so the state is changed to RESTARTING state by webserver process.
5. From now on, even if we restart scheduler, the task will never get scheduled or change its state. It needs to have its state manually fixed, e.g. by clearing it again.

A recording of steps to reproduce on local environment:
https://vimeo.com/857192666?share=copy

### Operating System

MacOS Ventura 13.4.1

### Versions of Apache Airflow Providers

N/A

### Deployment

Official Apache Airflow Helm Chart

### Deployment details

N/A

### 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)

"""
        Tests that backfill tasks won't get executed.
        """
        dag_id = "SchedulerJobTest.test_execute_task_instances_backfill_tasks_wont_execute"
        task_id_1 = "dummy_task"
        with dag_maker(dag_id=dag_id):
            task1 = EmptyOperator(task_id=task_id_1)
        scheduler_job = Job()
        self.job_runner = SchedulerJobRunner(job=scheduler_job, subdir=os.devnull)
        session = settings.Session()
        dr1 = dag_maker.create_dagrun(run_type=DagRunType.BACKFILL_JOB)
        ti1 = TaskInstance(task1, run_id=dr1.run_id)
        ti1.refresh_from_db()
        ti1.state = State.SCHEDULED
        session.merge(ti1)
        session.flush()
        assert dr1.is_backfill
        self.job_runner._critical_section_enqueue_task_instances(session)
        session.flush()
        ti1.refresh_from_db()
        assert State.SCHEDULED == ti1.state
        session.rollback()
    @conf_vars({("scheduler", "standalone_dag_processor"): "False"})
    def test_setup_callback_sink_not_standalone_dag_processor(self):