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
execute_callable = partial(execute_callable, **self.next_kwargs)
        
        
        if task_copy.execution_timeout:
            
            
            if self.next_method:
                timeout_seconds = (
                    task_copy.execution_timeout - (timezone.utcnow() - self.start_date)
                ).total_seconds()
            else:
                timeout_seconds = task_copy.execution_timeout.total_seconds()
            try:
                
                if timeout_seconds <= 0:
                    raise AirflowTaskTimeout()
                
                with timeout(timeout_seconds):
                    result = execute_callable(context=context)
            except AirflowTaskTimeout:
                task_copy.on_kill()
                raise
        else:
            result = execute_callable(context=context)
        
        if task_copy.do_xcom_push and result is not None:
            self.xcom_push(key=XCOM_RETURN_KEY, value=result)
        return result
    @provide_session
    def _defer_task(self, session, defer: TaskDeferred):