### 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)

cls._context_managed_dags.appendleft(dag)
    @classmethod
    def pop_context_managed_dag(cls) -> DAG | None:
        dag = cls._context_managed_dags.popleft()
        
        if cls.current_autoregister_module_name is not None and dag and dag.auto_register:
            mod = sys.modules[cls.current_autoregister_module_name]
            cls.autoregistered_dags.add((dag, mod))
        return dag
    @classmethod
    def get_current_dag(cls) -> DAG | None:
        try:
            return cls._context_managed_dags[0]
        except IndexError:
            return None
def _triggerer_is_healthy():
    from airflow.jobs.triggerer_job_runner import TriggererJobRunner
    job = TriggererJobRunner.most_recent_job()
    return job and job.is_alive()
def _run_task(ti: TaskInstance, session) -> TaskReturnCode | None: