### 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)

return task_id in self.task_dict
    def has_task_group(self, task_group_id: str) -> bool:
        return task_group_id in self.task_group_dict
    @functools.cached_property
    def task_group_dict(self):
        return {k: v for k, v in self._task_group.get_task_group_dict().items() if k is not None}
    def get_task(self, task_id: str, include_subdags: bool = False) -> Operator:
        if task_id in self.task_dict:
            return self.task_dict[task_id]
        if include_subdags:
            for dag in self.subdags:
                if task_id in dag.task_dict:
                    return dag.task_dict[task_id]
        raise TaskNotFound(f"Task {task_id} not found")
    def pickle_info(self):