### 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)

"""Generates a URL to the Graph view for a DagRun."""
    dag_id = attr.get("dag_id")
    run_id = attr.get("run_id")
    execution_date = attr.get("dag_run.execution_date") or attr.get("execution_date")
    url = url_for("Airflow.graph", dag_id=dag_id, run_id=run_id, execution_date=execution_date)
    return Markup('<a href="{url}">{run_id}</a>').format(url=url, run_id=run_id)
def _get_run_ordering_expr(name: str) -> ColumnOperators:
    expr = DagRun.__table__.columns[name]
    
    
    
    
    
    if name in ("data_interval_start", "data_interval_end"):
        expr = func.coalesce(expr, DagRun.execution_date)
    return expr.desc()
def sorted_dag_runs(query: Query, *, ordering: Sequence[str], limit: int) -> Sequence[DagRun]:
    """Produce DAG runs sorted by specified columns.
    :param query: An ORM query object against *DagRun*.
    :param ordering: Column names to sort the runs. should generally come from a
        timetable's ``run_ordering``.
    :param limit: Number of runs to limit to.
    :return: A list of DagRun objects ordered by the specified columns. The list
        contains only the *last* objects, but in *ascending* order.
    """
    ordering_exprs = (_get_run_ordering_expr(name) for name in ordering)
    runs = query.order_by(*ordering_exprs, DagRun.id.desc()).limit(limit).all()
    runs.reverse()
    return runs
def format_map_index(attr: dict) -> str: