### 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)

data_interval = None
        if isinstance(last_automated_dagrun, datetime):
            warnings.warn(
                "Passing a datetime to DAG.next_dagrun_info is deprecated. Use a DataInterval instead.",
                RemovedInAirflow3Warning,
                stacklevel=2,
            )
            data_interval = self.infer_automated_data_interval(
                timezone.coerce_datetime(last_automated_dagrun)
            )
        else:
            data_interval = last_automated_dagrun
        if restricted:
            restriction = self._time_restriction
        else:
            restriction = TimeRestriction(earliest=None, latest=None, catchup=True)
        try:
            info = self.timetable.next_dagrun_info(
                last_automated_data_interval=data_interval,
                restriction=restriction,
            )
        except Exception:
            self.log.exception(
                "Failed to fetch run info after data interval %s for DAG %r",
                data_interval,
                self.dag_id,
            )
            info = None
        return info
    def next_dagrun_after_date(self, date_last_automated_dagrun: pendulum.DateTime | None):