### 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)

"""Custom interface to allow faster deletion.
    The ``delete`` and ``delete_all`` methods are overridden to speed up
    deletion when a DAG run has a lot of related task instances. Relying on
    SQLAlchemy's cascading deletion is comparatively slow in this situation.
    """
    def delete(self, item: Model, raise_exception: bool = False) -> bool:
        self.session.query(TaskInstance).where(TaskInstance.run_id == item.run_id).delete()
        return super().delete(item, raise_exception=raise_exception)
    def delete_all(self, items: list[Model]) -> bool:
        self.session.query(TaskInstance).where(
            TaskInstance.run_id.in_(item.run_id for item in items)
        ).delete()
        return super().delete_all(items)
FieldConverter.conversion_table = (
    ("is_utcdatetime", DateTimeWithTimezoneField, AirflowDateTimePickerWidget),
) + FieldConverter.conversion_table
class UIAlert: