### 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)

f = attr.get(attr_name)
        return datetime_html(f)
    return dt
def datetime_html(dttm: DateTime | None) -> str:
    """Return an HTML formatted string with time element to support timezone changes in UI."""
    as_iso = dttm.isoformat() if dttm else ""
    if not as_iso:
        return Markup("")
    as_iso_short = as_iso
    if timezone.utcnow().isoformat()[:4] == as_iso[:4]:
        as_iso_short = as_iso[5:]
    
    return Markup('<nobr><time title="" datetime="{}">{}</time></nobr>').format(as_iso, as_iso_short)
def json_f(attr_name):
    """Returns a formatted string with HTML for given JSON serializable."""
    def json_(attr):
        f = attr.get(attr_name)
        serialized = json.dumps(f)
        return Markup("<nobr>{}</nobr>").format(serialized)
    return json_
def dag_link(attr):
    """Generates a URL to the Graph view for a Dag."""
    dag_id = attr.get("dag_id")
    execution_date = attr.get("execution_date")
    if not dag_id:
        return Markup("None")
    url = url_for("Airflow.graph", dag_id=dag_id, execution_date=execution_date)
    return Markup('<a href="{}">{}</a>').format(url, dag_id)
def dag_run_link(attr):