### 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)

"""A list of columns to show in the Add form.
        This dynamically calculates additional fields from providers and add
        them to the backing list. This calculation is done exactly once (by
        checking we're referencing the class-level variable instead of the
        instance-level), and only after we enter the request context (to skip
        superfuluous checks done by Flask-Appbuilder on startup).
        """
        if self._add_columns is type(self)._add_columns and has_request_context():
            self._add_columns = [*self._add_columns, *(k for k, _ in self._iter_extra_field_names())]
        return self._add_columns
    @property
    def edit_columns(self) -> list[str]:
        """A list of columns to show in the Edit form.
        This dynamically calculates additional fields from providers and add
        them to the backing list. This calculation is done exactly once (by
        checking we're referencing the class-level variable instead of the
        instance-level), and only after we enter the request context (to skip
        superfuluous checks done by Flask-Appbuilder on startup).
        """
        if self._edit_columns is type(self)._edit_columns and has_request_context():
            self._edit_columns = [*self._edit_columns, *(k for k, _ in self._iter_extra_field_names())]
        return self._edit_columns
    @action("muldelete", "Delete", "Are you sure you want to delete selected records?", single=False)
    @auth.has_access(
        [
            (permissions.ACTION_CAN_EDIT, permissions.RESOURCE_DAG),
        ]
    )
    def action_muldelete(self, items):