### 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)

"""
    Run a single task instance, and push result to Xcom for downstream tasks.
    Bypasses a lot of extra steps used in `task.run` to keep our local running as fast as
    possible.  This function is only meant for the `dag.test` function as a helper function.
    Args:
        ti: TaskInstance to run
    """
    ret = None
    log.info("*****************************************************")
    if ti.map_index > 0:
        log.info("Running task %s index %d", ti.task_id, ti.map_index)
    else:
        log.info("Running task %s", ti.task_id)
    try:
        ret = ti._run_raw_task(session=session)
        session.flush()
        log.info("%s ran successfully!", ti.task_id)
    except AirflowSkipException:
        log.info("Task Skipped, continuing")
    log.info("*****************************************************")
    return ret
def _get_or_create_dagrun(
    dag: DAG,
    conf: dict[Any, Any] | None,
    start_date: datetime,
    execution_date: datetime,
    run_id: str,
    session: Session,