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.
airflow/models/taskinstance.py
'prev_data_interval_end_success': lazy_object_proxy.Proxy(get_prev_data_interval_end_success),
            'prev_ds': deprecated_proxy(get_prev_ds, key="prev_ds"),
            'prev_ds_nodash': deprecated_proxy(get_prev_ds_nodash, key="prev_ds_nodash"),
            'prev_execution_date': deprecated_proxy(get_prev_execution_date, key='prev_execution_date'),
            'prev_execution_date_success': deprecated_proxy(
                lambda: self.get_previous_execution_date(state=State.SUCCESS, session=session),
                key='prev_execution_date_success',
                replacement='prev_data_interval_start_success',
            ),
            'prev_start_date_success': lazy_object_proxy.Proxy(get_prev_start_date_success),
            'run_id': dag_run.run_id,
            'task': task,
            'task_instance': self,
            'task_instance_key_str': f"{task.dag_id}__{task.task_id}__{ds_nodash}",
            'test_mode': self.test_mode,
            'ti': self,
            'tomorrow_ds': deprecated_proxy(get_tomorrow_ds, key='tomorrow_ds'),
            'tomorrow_ds_nodash': deprecated_proxy(get_tomorrow_ds_nodash, key='tomorrow_ds_nodash'),
            'ts': ts,
            'ts_nodash': ts_nodash,
            'ts_nodash_with_tz': ts_nodash_with_tz,
            'var': {
                'json': VariableJsonAccessor(),
                'value': VariableAccessor(),
            },
            'conn': ConnectionAccessor(),
            'yesterday_ds': deprecated_proxy(get_yesterday_ds, key='yesterday_ds'),
            'yesterday_ds_nodash': deprecated_proxy(get_yesterday_ds_nodash, key='yesterday_ds_nodash'),
        }
    def get_rendered_template_fields(self):