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/models/test_taskinstance.py
done=done,
            flag_upstream_failed=flag_upstream_failed,
        )
        completed = all(dep.passed for dep in dep_results)
        assert completed == expect_completed
        assert ti.state == expect_state
    def test_respects_prev_dagrun_dep(self, create_dummy_dag):
        _, task = create_dummy_dag(dag_id='test_dag')
        ti = TI(task, DEFAULT_DATE)
        failing_status = [TIDepStatus('test fail status name', False, 'test fail reason')]
        passing_status = [TIDepStatus('test pass status name', True, 'test passing reason')]
        with patch(
            'airflow.ti_deps.deps.prev_dagrun_dep.PrevDagrunDep.get_dep_statuses', return_value=failing_status
        ):
            assert not ti.are_dependencies_met()
        with patch(
            'airflow.ti_deps.deps.prev_dagrun_dep.PrevDagrunDep.get_dep_statuses', return_value=passing_status
        ):
            assert ti.are_dependencies_met()
    @pytest.mark.parametrize(
        "downstream_ti_state, expected_are_dependents_done",
        [
            (State.SUCCESS, True),
            (State.SKIPPED, True),
            (State.RUNNING, False),
            (State.FAILED, False),
            (State.NONE, False),
        ],
    )
    def test_are_dependents_done(self, downstream_ti_state, expected_are_dependents_done, create_dummy_dag):