### 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)

"""
    This ModelView prevents ability to pass primary keys of objects relating to DAGs you shouldn't be able to
    edit. This only holds for the add, update and delete operations.
    You will still need to use the `action_has_dag_edit_access()` for actions.
    """
    @staticmethod
    def validate_dag_edit_access(item: DagRun | TaskInstance):
        """Validates whether the user has 'can_edit' access for this specific DAG."""
        if not get_airflow_app().appbuilder.sm.can_edit_dag(item.dag_id):
            raise AirflowException(f"Access denied for dag_id {item.dag_id}")
    def pre_add(self, item: DagRun | TaskInstance):
        self.validate_dag_edit_access(item)
    def pre_update(self, item: DagRun | TaskInstance):
        self.validate_dag_edit_access(item)
    def pre_delete(self, item: DagRun | TaskInstance):
        self.validate_dag_edit_access(item)
    def post_add_redirect(self):  
        return redirect(self.get_default_url())
    def post_edit_redirect(self):  
        return redirect(self.get_default_url())
    def post_delete_redirect(self):