### 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 restful endpoint that returns external links for a given Operator.
        It queries the operator that sent the request for the links it wishes
        to provide for a given external link name.
        API: GET
        Args: dag_id: The id of the dag containing the task in question
              task_id: The id of the task in question
              execution_date: The date of execution of the task
              link_name: The name of the link reference to find the actual URL for
        Returns:
            200: {url: <url of link>, error: None} - returned when there was no problem
                finding the URL
            404: {url: None, error: <error message>} - returned when the operator does
                not return a URL
        """
        dag_id = request.args.get("dag_id")
        task_id = request.args.get("task_id")
        map_index = request.args.get("map_index", -1, type=int)
        execution_date = request.args.get("execution_date")
        dttm = _safe_parse_datetime(execution_date)
        dag = get_airflow_app().dag_bag.get_dag(dag_id)
        if not dag or task_id not in dag.task_ids:
            return {"url": None, "error": f"can't find dag {dag} or task_id {task_id}"}, 404
        task: AbstractOperator = dag.get_task(task_id)
        link_name = request.args.get("link_name")