### 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)

dag_warnings = session.query(DagWarning).filter(DagWarning.dag_id == dag_id).all()
    if dag_warnings:
        for dag_warning in dag_warnings:
            flash(dag_warning.message, "warning")
def get_sensitive_variables_fields():
    import warnings
    from airflow.utils.log.secrets_masker import get_sensitive_variables_fields
    warnings.warn(
        "This function is deprecated. Please use "
        "`airflow.utils.log.secrets_masker.get_sensitive_variables_fields`",
        RemovedInAirflow3Warning,
        stacklevel=2,
    )
    return get_sensitive_variables_fields()
def should_hide_value_for_key(key_name):
    import warnings
    from airflow.utils.log.secrets_masker import should_hide_value_for_key
    warnings.warn(
        "This function is deprecated. Please use "
        "`airflow.utils.log.secrets_masker.should_hide_value_for_key`",
        RemovedInAirflow3Warning,
        stacklevel=2,
    )
    return should_hide_value_for_key(key_name)
def get_params(**kwargs):
    """Return URL-encoded params."""
    return urlencode({d: v for d, v in kwargs.items() if v is not None}, True)
def generate_pages(