### Apache Airflow version

2.7.0rc1

### What happened

As per https://github.com/apache/airflow/pull/31583, now we can only run DAG with config from UI if DAG has params, however, if a DAG is using dag_run.conf there is no way to run with config from UI and as dag_run.conf is not deprecated most of the users will be impacted by this

@hussein-awala  also mentioned it in his [voting](https://lists.apache.org/thread/zd9ppxw1xwxsl66w0tyw1wch9flzb03w)

### What you think should happen instead

I think there should be a way to provide param values from UI when dag_run.conf is used in DAG

### How to reproduce

Use below DAG in 2.7.0rc and you will notice there is no way to provide conf value from airflow UI

DAG CODE

```
from airflow.models import DAG
from airflow.operators.bash import BashOperator
from airflow.operators.python import PythonOperator
from airflow.utils.dates import days_ago

dag = DAG(
dag_id="trigger_target_dag",
default_args={"start_date": days_ago(2), "owner": "Airflow"},
tags=["core"],
schedule_interval=None, # This must be none so it's triggered by the controller
is_paused_upon_creation=False, # This must be set so other workers can pick this dag up. mabye it's a bug idk
)

def run_this_func(**context):
print(
f"Remotely received value of {context['dag_run'].conf['message']} for key=message "
)

run_this = PythonOperator(
task_id="run_this",
python_callable=run_this_func,
dag=dag,
)

bash_task = BashOperator(
task_id="bash_task",
bash_command='echo "Here is the message: $message"',
env={"message": '{{ dag_run.conf["message"] if dag_run else "" }}'},
dag=dag,
)
```

### Operating System

MAS os Monterey

### Versions of Apache Airflow Providers

_No response_

### Deployment

Astronomer

### Deployment details

_No response_

### 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)

owner_links_dict = DagOwnerAttributes.get_all(session)
            import_errors = select(errors.ImportError).order_by(errors.ImportError.id)
            if (permissions.ACTION_CAN_READ, permissions.RESOURCE_DAG) not in user_permissions:
                
                import_errors = import_errors.join(
                    DagModel, DagModel.fileloc == errors.ImportError.filename
                ).where(DagModel.dag_id.in_(filter_dag_ids))
            import_errors = session.scalars(import_errors)
            for import_error in import_errors:
                flash(
                    f"Broken DAG: [{import_error.filename}] {import_error.stacktrace}",
                    "dag_import_error",
                )
        from airflow.plugins_manager import import_errors as plugin_import_errors
        for filename, stacktrace in plugin_import_errors.items():
            flash(
                f"Broken plugin: [{filename}] {stacktrace}",
                "error",
            )
        num_of_pages = math.ceil(num_of_all_dags / dags_per_page)
        state_color_mapping = State.state_color.copy()
        state_color_mapping["null"] = state_color_mapping.pop(None)
        page_title = conf.get(section="webserver", key="instance_name", fallback="DAGs")
        page_title_has_markup = conf.getboolean(
            section="webserver", key="instance_name_has_markup", fallback=False
        )
        dashboard_alerts = [
            fm for fm in settings.DASHBOARD_UIALERTS if fm.should_show(get_airflow_app().appbuilder.sm)
        ]
        def _iter_parsed_moved_data_table_names():