### 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)

"""Form widget used to display connection."""
    @cached_property
    def field_behaviours(self) -> str:
        return json.dumps(ProvidersManager().field_behaviours)
    @cached_property
    def testable_connection_types(self) -> list[str]:
        return [
            connection_type
            for connection_type, hook_info in ProvidersManager().hooks.items()
            if hook_info and hook_info.connection_testable
        ]
class ConnectionFormProxy:
    """A stand-in for the connection form class.
    Flask-Appbuilder model views only ever call the ``refresh()`` function on
    the form class, so this is the perfect place to make the form generation
    dynamic. See docstring of ``create_connection_form_class`` for rationales.
    """
    @staticmethod
    def refresh(obj=None):
        return create_connection_form_class().refresh(obj)
class ConnectionModelView(AirflowModelView):