Currently we use execution-date when generating the command to send via executor in https://github.com/apache/airflow/blob/9c94b72d440b18a9e42123d20d48b951712038f9/airflow/models/taskinstance.py#L420-L436

We should replace the execution_date in their to run_id instead and handle the corresponding changes needs on the executor and worker.
tests/jobs/test_local_task_job.py
with success_callback_called.get_lock():
                success_callback_called.value = 1
            assert context['dag_run'].dag_id == 'test_mark_success'
        def task_function(ti):
            assert ti.state == State.RUNNING
            
            ti.state = State.SUCCESS
            session.merge(ti)
            session.commit()
            
            time.sleep(10)
            assert False
        with dag_maker(dag_id='test_mark_success', start_date=DEFAULT_DATE, default_args={'owner': 'owner1'}):
            task = PythonOperator(
                task_id='test_state_succeeded1',
                python_callable=task_function,
                on_success_callback=success_callback,
            )
        dag_maker.create_dagrun()
        ti = TaskInstance(task=task, execution_date=DEFAULT_DATE)
        ti.refresh_from_db()
        job1 = LocalTaskJob(task_instance=ti, ignore_ti_state=True, executor=SequentialExecutor())
        def dummy_return_code(*args, **kwargs):