### 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)

"""
    Parse datetime and return error message for invalid dates.
    :param v: the string value to be parsed
    :param allow_empty: Set True to return none if empty str or None
    """
    if allow_empty is True and not v:
        return None
    try:
        return timezone.parse(v)
    except (TypeError, ParserError):
        abort(400, f"Invalid datetime: {v!r}")
def node_dict(node_id, label, node_class):
    return {
        "id": node_id,
        "value": {"label": label, "rx": 5, "ry": 5, "class": node_class},
    }
def dag_to_grid(dag: DagModel, dag_runs: Sequence[DagRun], session: Session):
    """
    Create a nested dict representation of the DAG's TaskGroup and its children
    used to construct the Graph and Grid views.
    """
    query = (
        session.query(
            TaskInstance.task_id,