### 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)

self,
        task_ids_or_regex: str | Pattern | Iterable[str],
        include_downstream=False,
        include_upstream=True,
        include_direct_upstream=False,
    ):
        """
        Return a subset of the current dag based on regex matching one or more tasks.
        Returns a subset of the current dag as a deep copy of the current dag
        based on a regex that should match one or many tasks, and includes
        upstream and downstream neighbours based on the flag passed.
        :param task_ids_or_regex: Either a list of task_ids, or a regex to
            match against task ids (as a string, or compiled regex pattern).
        :param include_downstream: Include all downstream tasks of matched
            tasks, in addition to matched tasks.
        :param include_upstream: Include all upstream tasks of matched tasks,
            in addition to matched tasks.
        :param include_direct_upstream: Include all tasks directly upstream of matched
            and downstream (if include_downstream = True) tasks
        """
        from airflow.models.baseoperator import BaseOperator
        from airflow.models.mappedoperator import MappedOperator
        
        
        memo = {id(self.task_dict): None, id(self._task_group): None}
        dag = copy.deepcopy(self, memo)  
        if isinstance(task_ids_or_regex, (str, Pattern)):
            matched_tasks = [t for t in self.tasks if re2.findall(task_ids_or_regex, t.task_id)]
        else: