### 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)

f"A {run_type.value} DAG run cannot use ID {run_id!r} since it "
                    f"is reserved for {inferred_run_type.value} runs"
                )
        elif run_type and logical_date is not None:  
            run_id = self.timetable.generate_run_id(
                run_type=run_type, logical_date=logical_date, data_interval=data_interval
            )
        else:
            raise AirflowException(
                "Creating DagRun needs either `run_id` or both `run_type` and `execution_date`"
            )
        regex = airflow_conf.get("scheduler", "allowed_run_id_pattern")
        if run_id and not re2.match(RUN_ID_REGEX, run_id):
            if not regex.strip() or not re2.match(regex.strip(), run_id):
                raise AirflowException(
                    f"The provided run ID '{run_id}' is invalid. It does not match either "
                    f"the configured pattern: '{regex}' or the built-in pattern: '{RUN_ID_REGEX}'"
                )
        
        copied_params = copy.deepcopy(self.params)
        copied_params.update(conf or {})
        copied_params.validate()
        run = DagRun(
            dag_id=self.dag_id,
            run_id=run_id,
            execution_date=logical_date,
            start_date=start_date,
            external_trigger=external_trigger,
            conf=conf,
            state=state,