### What do you see as an issue?

The [/dags/{dag_id}/details](https://airflow.apache.org/docs/apache-airflow/stable/stable-rest-api-ref.html#operation/post_set_task_instances_state) endpoint of the REST API does not return all of the keys that are listed in the documentation. If I run `curl -X GET localhost:8080/api/v1/dags/{my_dag}/details`, then compare the results with the results in the documentation, you can see the following missing keys:

```python
>>> for key in docs.keys():
...     if not key in actual.keys():
...             print(key)
...
root_dag_id
last_parsed_time
last_pickled
last_expired
scheduler_lock
timetable_description
has_task_concurrency_limits
has_import_errors
next_dagrun
next_dagrun_data_interval_start
next_dagrun_data_interval_end
next_dagrun_create_after
template_search_path
```

### Solving the problem

Either remove these keys from the documentation or fix the API endpoint

### Anything else

_No response_

### Are you willing to submit PR?

- [ ] Yes I am willing to submit a PR!

### Code of Conduct

- [X] I agree to follow this project's [Code of Conduct](https://github.com/apache/airflow/blob/main/CODE_OF_CONDUCT.md)

existing_dags.get(dag_id)
                and existing_dags.get(dag_id).schedule_dataset_references  
                or []
            )
            dag_refs_to_add = {x for x in dag_refs_needed if x not in dag_refs_stored}
            session.bulk_save_objects(dag_refs_to_add)
            for obj in dag_refs_stored - dag_refs_needed:
                session.delete(obj)
        existing_task_outlet_refs_dict = collections.defaultdict(set)
        for dag_id, orm_dag in existing_dags.items():
            for todr in orm_dag.task_outlet_dataset_references:
                existing_task_outlet_refs_dict[(dag_id, todr.task_id)].add(todr)
        
        for (dag_id, task_id), uri_list in outlet_references.items():
            task_refs_needed = {
                TaskOutletDatasetReference(dataset_id=stored_datasets[uri].id, dag_id=dag_id, task_id=task_id)
                for uri in uri_list
            }
            task_refs_stored = existing_task_outlet_refs_dict[(dag_id, task_id)]
            task_refs_to_add = {x for x in task_refs_needed if x not in task_refs_stored}
            session.bulk_save_objects(task_refs_to_add)
            for obj in task_refs_stored - task_refs_needed:
                session.delete(obj)
        
        
        session.flush()
        for dag in dags:
            cls.bulk_write_to_db(dag.subdags, processor_subdir=processor_subdir, session=session)
    @provide_session
    def sync_to_db(self, processor_subdir: str | None = None, session=NEW_SESSION):