### 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 num_active_runs.get(dag.dag_id, 0) >= orm_dag.max_active_runs:
                orm_dag.next_dagrun_create_after = None
            else:
                orm_dag.calculate_dagrun_date_fields(dag, last_automated_data_interval)
            dag_tags = set(dag.tags or {})
            orm_dag_tags = list(orm_dag.tags or [])
            for orm_tag in orm_dag_tags:
                if orm_tag.name not in dag_tags:
                    session.delete(orm_tag)
                    orm_dag.tags.remove(orm_tag)
            orm_tag_names = {t.name for t in orm_dag_tags}
            for dag_tag in dag_tags:
                if dag_tag not in orm_tag_names:
                    dag_tag_orm = DagTag(name=dag_tag, dag_id=dag.dag_id)
                    orm_dag.tags.append(dag_tag_orm)
                    session.add(dag_tag_orm)
            orm_dag_links = orm_dag.dag_owner_links or []
            for orm_dag_link in orm_dag_links:
                if orm_dag_link not in dag.owner_links:
                    session.delete(orm_dag_link)
            for owner_name, owner_link in dag.owner_links.items():
                dag_owner_orm = DagOwnerAttributes(dag_id=dag.dag_id, owner=owner_name, link=owner_link)
                session.add(dag_owner_orm)
        DagCode.bulk_sync_to_db(filelocs, session=session)
        from airflow.datasets import Dataset
        from airflow.models.dataset import (
            DagScheduleDatasetReference,
            DatasetModel,
            TaskOutletDatasetReference,
        )