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
assert ti.state == State.RUNNING
            
            ti.state = State.SUCCESS
            session.merge(ti)
            session.commit()
            
            time.sleep(10)
        with dag_maker('test_mark_success'):
            task1 = PythonOperator(task_id="task1", python_callable=task_function)
        dag_maker.create_dagrun()
        ti = TaskInstance(task=task1, execution_date=DEFAULT_DATE)
        ti.refresh_from_db()
        job1 = LocalTaskJob(task_instance=ti, ignore_ti_state=True)
        def dummy_return_code(*args, **kwargs):
            return None if not job1.terminating else -9
        
        mock_return_code.side_effect = dummy_return_code
        with timeout(30):
            job1.run()
        ti.refresh_from_db()
        assert State.SUCCESS == ti.state
        assert (
            "State of this instance has been externally set to success. Terminating instance." in caplog.text
        )
    def test_localtaskjob_double_trigger(self):