### Description

Going to Airflow web UI, Browse>DAG Run displays the list of runs, but there is no way to search or filter based on the text in the "Note" column.

### Use case/motivation

It is possible to do a free text search for the "Run Id" field. The Note field may contain pieces of information that may be relevant to find, or to filter on the basis of these notes.

### Related issues

Sorting by Note in List Dag Run fails: 
https://github.com/apache/airflow/issues/30041

### Are you willing to submit a 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)

"""Deletes DAG."""
        from airflow.api.common import delete_dag
        from airflow.exceptions import DagNotFound
        dag_id = request.values.get("dag_id")
        origin = get_safe_url(request.values.get("origin"))
        redirect_url = get_safe_url(request.values.get("redirect_url"))
        try:
            delete_dag.delete_dag(dag_id)
        except DagNotFound:
            flash(f"DAG with id {dag_id} not found. Cannot delete", "error")
            return redirect(redirect_url)
        except AirflowException:
            flash(
                f"Cannot delete DAG with id {dag_id} because some task instances of the DAG "
                "are still running. Please mark the  task instances as "
                "failed/succeeded before deleting the DAG",
                "error",
            )
            return redirect(redirect_url)
        flash(f"Deleting DAG with id {dag_id}. May take a couple minutes to fully disappear.")
        
        return redirect(origin)
    @expose("/trigger", methods=["POST", "GET"])
    @auth.has_access(
        [
            (permissions.ACTION_CAN_EDIT, permissions.RESOURCE_DAG),