### 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)

if not dag_bag:
                        from airflow.models.dagbag import DagBag
                        dag_bag = DagBag(read_dags_from_db=True)
                    external_dag = dag_bag.get_dag(tii.dag_id, session=session)
                    if not external_dag:
                        raise AirflowException(f"Could not find dag {tii.dag_id}")
                    downstream = external_dag.partial_subset(
                        task_ids_or_regex=[tii.task_id],
                        include_upstream=False,
                        include_downstream=True,
                    )
                    result.update(
                        downstream._get_task_instances(
                            task_ids=None,
                            run_id=tii.run_id,
                            start_date=None,
                            end_date=None,
                            state=state,
                            include_subdags=include_subdags,
                            include_dependent_dags=include_dependent_dags,
                            include_parentdag=False,
                            as_pk_tuple=True,
                            exclude_task_ids=exclude_task_ids,
                            dag_bag=dag_bag,
                            session=session,
                            recursion_depth=recursion_depth + 1,
                            max_recursion_depth=max_recursion_depth,
                            visited_external_tis=visited_external_tis,
                        )
                    )