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
merge_conn(
                Connection(
                    conn_id="a_connection",
                    conn_type="a_type",
                    description="a_conn_description",
                    host="hostvalue",
                    login="loginvalue",
                    password="passwordvalue",
                    schema="schemavalues",
                    extra={
                        "extra__asana__workspace": "extra1",
                    },
                ),
                session,
            )
        _, task = create_dummy_dag()
        ti = TI(task=task, execution_date=DEFAULT_DATE)
        context = ti.get_template_context()
        result = task.render_template(content, context)
        assert result == expected_output
    @pytest.mark.parametrize(
        "content, expected_output",
        [
            ('{{ var.value.a_variable }}', 'a test value'),
            ('{{ var.value.get("a_variable") }}', 'a test value'),
            ('{{ var.value.get("a_variable", "unused_fallback") }}', 'a test value'),
            ('{{ var.value.get("missing_variable", "fallback") }}', 'fallback'),
        ],
    )
    def test_template_with_variable(self, content, expected_output, create_dummy_dag):