### 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)

.join(
                    subq_failed,
                    and_(
                        subq_all.c.dag_id == subq_failed.c.dag_id,
                        subq_all.c.start_date == subq_failed.c.start_date,
                    ),
                )
                .subquery()
            )
            failed_dags = dags_query.join(subq_join, DagModel.dag_id == subq_join.c.dag_id)
            is_paused_count = dict(
                session.execute(
                    select(DagModel.is_paused, func.count(DagModel.dag_id)).group_by(DagModel.is_paused)
                ).all()
            )
            status_count_active = is_paused_count.get(False, 0)
            status_count_paused = is_paused_count.get(True, 0)
            status_count_running = get_query_count(running_dags, session=session)
            status_count_failed = get_query_count(failed_dags, session=session)
            all_dags_count = status_count_active + status_count_paused
            if arg_status_filter == "active":
                current_dags = active_dags
                num_of_all_dags = status_count_active
            elif arg_status_filter == "paused":
                current_dags = paused_dags
                num_of_all_dags = status_count_paused
            elif arg_status_filter == "running":
                current_dags = running_dags
                num_of_all_dags = status_count_running
            elif arg_status_filter == "failed":