### 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)

matched_tasks = [t for t in self.tasks if t.task_id in task_ids_or_regex]
        also_include_ids: set[str] = set()
        for t in matched_tasks:
            if include_downstream:
                for rel in t.get_flat_relatives(upstream=False):
                    also_include_ids.add(rel.task_id)
                    if rel not in matched_tasks:  
                        
                        
                        if not rel.is_setup and not rel.is_teardown:
                            also_include_ids.update(
                                x.task_id for x in rel.get_upstreams_only_setups_and_teardowns()
                            )
            if include_upstream:
                also_include_ids.update(x.task_id for x in t.get_upstreams_follow_setups())
            else:
                if not t.is_setup and not t.is_teardown:
                    also_include_ids.update(x.task_id for x in t.get_upstreams_only_setups_and_teardowns())
            if t.is_setup and not include_downstream:
                also_include_ids.update(x.task_id for x in t.downstream_list if x.is_teardown)
        also_include: list[Operator] = [self.task_dict[x] for x in also_include_ids]
        direct_upstreams: list[Operator] = []
        if include_direct_upstream:
            for t in itertools.chain(matched_tasks, also_include):
                upstream = (u for u in t.upstream_list if isinstance(u, (BaseOperator, MappedOperator)))
                direct_upstreams.extend(upstream)
        
        
        
        def _deepcopy_task(t) -> Operator: