### 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)

task_ids: list[str | tuple[str, int]] = []
        end_date = execution_date if not future else None
        start_date = execution_date if not past else None
        locked_dag_run_ids: list[int] = []
        if group_id is not None:
            task_group_dict = dag.task_group.get_task_group_dict()
            task_group = task_group_dict.get(group_id)
            if task_group is None:
                return redirect_or_json(
                    origin, msg=f"TaskGroup {group_id} could not be found", status="error", status_code=404
                )
            task_ids = task_ids_or_regex = [t.task_id for t in task_group.iter_tasks()]
            
            
            dag_runs_query = session.query(DagRun.id).filter(DagRun.dag_id == dag_id).with_for_update()
            if start_date is None and end_date is None:
                dag_runs_query = dag_runs_query.filter(DagRun.execution_date == start_date)
            else:
                if start_date is not None:
                    dag_runs_query = dag_runs_query.filter(DagRun.execution_date >= start_date)
                if end_date is not None:
                    dag_runs_query = dag_runs_query.filter(DagRun.execution_date <= end_date)
            locked_dag_run_ids = dag_runs_query.all()
        elif task_id:
            if map_indexes is None:
                task_ids = [task_id]
            else:
                task_ids = [(task_id, map_index) for map_index in map_indexes]
            task_ids_or_regex = [task_id]
        dag = dag.partial_subset(