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
def test_task_exit_should_update_state_of_finished_dagruns_with_dag_paused(self, dag_maker):
        """Test that with DAG paused, DagRun state will update when the tasks finishes the run"""
        with dag_maker(dag_id='test_dags') as dag:
            op1 = PythonOperator(task_id='dummy', python_callable=lambda: True)
        session = settings.Session()
        dagmodel = dag_maker.dag_model
        dagmodel.next_dagrun_create_after = dag.following_schedule(DEFAULT_DATE)
        dagmodel.is_paused = True
        session.merge(dagmodel)
        session.flush()
        
        dagbag = DagBag(dag_folder="/dev/null", include_examples=False, read_dags_from_db=False)
        dagbag.bag_dag(dag, root_dag=dag)
        dagbag.sync_to_db()
        dr = dag_maker.create_dagrun(run_type=DagRunType.SCHEDULED)
        assert dr.state == State.RUNNING
        ti = TaskInstance(op1, dr.execution_date)
        job1 = LocalTaskJob(task_instance=ti, ignore_ti_state=True, executor=SequentialExecutor())
        job1.task_runner = StandardTaskRunner(job1)
        job1.run()
        session.add(dr)
        session.refresh(dr)
        assert dr.state == State.SUCCESS
@pytest.fixture()
def clean_db_helper():
    yield
    db.clear_db_jobs()
    db.clear_db_runs()
@pytest.mark.usefixtures("clean_db_helper")
class TestLocalTaskJobPerformance: