### Body

Currently `start_date` is mandatory parameter.
For DAGs with `schedule=None` we can relax this requirement as no scheduling calculation needed so the `start_date` parameter isn't used.

### Committer

- [X] I acknowledge that I am a maintainer/committer of the Apache Airflow project.
tis_for_dagrun_state = self._tis_for_dagrun_state(dag=dag, tis=tis)
        
        if not unfinished.tis and any(x.state in State.failed_states for x in tis_for_dagrun_state):
            self.log.error("Marking run %s failed", self)
            self.set_state(DagRunState.FAILED)
            self.notify_dagrun_state_changed(msg="task_failure")
            if execute_callbacks:
                dag.handle_callback(self, success=False, reason="task_failure", session=session)
            elif dag.has_on_failure_callback:
                from airflow.models.dag import DagModel
                dag_model = DagModel.get_dagmodel(dag.dag_id, session)
                callback = DagCallbackRequest(
                    full_filepath=dag.fileloc,
                    dag_id=self.dag_id,
                    run_id=self.run_id,
                    is_failure_callback=True,
                    processor_subdir=None if dag_model is None else dag_model.processor_subdir,
                    msg="task_failure",
                )
        
        elif not unfinished.tis and all(x.state in State.success_states for x in tis_for_dagrun_state):
            self.log.info("Marking run %s successful", self)
            self.set_state(DagRunState.SUCCESS)
            self.notify_dagrun_state_changed(msg="success")
            if execute_callbacks:
                dag.handle_callback(self, success=True, reason="success", session=session)
            elif dag.has_on_success_callback:
                from airflow.models.dag import DagModel
                dag_model = DagModel.get_dagmodel(dag.dag_id, session)
                callback = DagCallbackRequest(