### 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)

_add_columns = _edit_columns = [
        "conn_id",
        "conn_type",
        "description",
        "host",
        "schema",
        "login",
        "password",
        "port",
        "extra",
    ]
    
    
    add_form = edit_form = ConnectionFormProxy
    add_template = "airflow/conn_create.html"
    edit_template = "airflow/conn_edit.html"
    add_widget = ConnectionFormWidget
    edit_widget = ConnectionFormWidget
    base_order = ("conn_id", "asc")
    def _iter_extra_field_names(self) -> Iterator[tuple[str, str]]:
        """Iterate through provider-backed connection fields.
        Note that this cannot be a property (including a cached property)
        because Flask-Appbuilder attempts to access all members on startup, and
        using a property would initialize the providers manager too eagerly.
        """
        return ((k, v.field_name) for k, v in ProvidersManager().connection_form_widgets.items())
    @property
    def add_columns(self) -> list[str]: