### 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)

.group_by(_convert_to_date(session, DagRun.execution_date), DagRun.state)
            .order_by(_convert_to_date(session, DagRun.execution_date).asc())
            .all()
        )
        data_dag_states = [
            {
                
                
                "date": dr.date if isinstance(dr.date, str) else dr.date.isoformat(),
                "state": dr.state,
                "count": dr.count,
            }
            for dr in dag_states
        ]
        if dag_states and dag_states[-1].data_interval_start and dag_states[-1].data_interval_end:
            last_automated_data_interval = DataInterval(
                timezone.coerce_datetime(dag_states[-1].data_interval_start),
                timezone.coerce_datetime(dag_states[-1].data_interval_end),
            )
            year = last_automated_data_interval.end.year
            restriction = TimeRestriction(dag.start_date, dag.end_date, False)
            dates: dict[datetime.date, int] = collections.Counter()
            if isinstance(dag.timetable, CronMixin):
                
                dates_iter: Iterator[datetime.datetime | None] = croniter(
                    dag.timetable._expression,
                    start_time=last_automated_data_interval.end,
                    ret_type=datetime.datetime,
                )
                for dt in dates_iter: