### 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)

dags: Collection[DAG],
        processor_subdir: str | None = None,
        session=NEW_SESSION,
    ):
        """
        Ensure the DagModel rows for the given dags are up-to-date in the dag table in the DB.
        Note that this method can be called for both DAGs and SubDAGs. A SubDag is actually a SubDagOperator.
        :param dags: the DAG objects to save to the DB
        :return: None
        """
        if not dags:
            return
        log.info("Sync %s DAGs", len(dags))
        dag_by_ids = {dag.dag_id: dag for dag in dags}
        dag_ids = set(dag_by_ids)
        query = (
            select(DagModel)
            .options(joinedload(DagModel.tags, innerjoin=False))
            .where(DagModel.dag_id.in_(dag_ids))
            .options(joinedload(DagModel.schedule_dataset_references))
            .options(joinedload(DagModel.task_outlet_dataset_references))
        )
        query = with_row_locks(query, of=DagModel, session=session)
        orm_dags: list[DagModel] = session.scalars(query).unique().all()
        existing_dags = {orm_dag.dag_id: orm_dag for orm_dag in orm_dags}
        missing_dag_ids = dag_ids.difference(existing_dags)
        for missing_dag_id in missing_dag_ids:
            orm_dag = DagModel(dag_id=missing_dag_id)
            dag = dag_by_ids[missing_dag_id]
            if dag.is_paused_upon_creation is not None: