### 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)

if get_airflow_app().appbuilder.sm.has_all_dags_access(g.user):
            return query
        filter_dag_ids = get_airflow_app().appbuilder.sm.get_accessible_dag_ids(g.user)
        return query.filter(self.model.dag_id.in_(filter_dag_ids))
class AirflowModelView(ModelView):
    """Airflow Mode View.
    Overridden `__getattribute__` to wraps REST methods with action_logger
    """
    list_widget = AirflowModelListWidget
    page_size = PAGE_SIZE
    CustomSQLAInterface = wwwutils.CustomSQLAInterface
    def __getattribute__(self, attr):
        """Wraps action REST methods with `action_logging` wrapper
        Overriding enables differentiating resource and generation of event name at the decorator level.
        if attr in ["show", "list", "read", "get", "get_list"]:
            return action_logging(event="RESOURCE_NAME"."action_name")(attr)
        else:
            return attr
        """
        attribute = object.__getattribute__(self, attr)
        if (
            callable(attribute)
            and hasattr(attribute, "_permission_name")
            and attribute._permission_name in self.method_permission_name
        ):
            permission_str = self.method_permission_name[attribute._permission_name]
            if permission_str not in ["show", "list", "read", "get", "get_list"]:
                return action_logging(event=f"{self.route_base.strip('/')}.{permission_str}")(attribute)
        return attribute
class AirflowPrivilegeVerifierModelView(AirflowModelView):