### 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)

"""Home view."""
        from airflow.models.dag import DagOwnerAttributes
        hide_paused_dags_by_default = conf.getboolean("webserver", "hide_paused_dags_by_default")
        default_dag_run = conf.getint("webserver", "default_dag_run_display_number")
        num_runs = request.args.get("num_runs", default=default_dag_run, type=int)
        current_page = request.args.get("page", default=0, type=int)
        arg_search_query = request.args.get("search")
        arg_tags_filter = request.args.getlist("tags")
        arg_status_filter = request.args.get("status")
        arg_sorting_key = request.args.get("sorting_key", "dag_id")
        arg_sorting_direction = request.args.get("sorting_direction", default="asc")
        if request.args.get("reset_tags") is not None:
            flask_session[FILTER_TAGS_COOKIE] = None
            
            return redirect(url_for("Airflow.index"))
        cookie_val = flask_session.get(FILTER_TAGS_COOKIE)
        if arg_tags_filter:
            flask_session[FILTER_TAGS_COOKIE] = ",".join(arg_tags_filter)