### 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)

"""
    Helper for alerts messages shown on the UI.
    :param message: The message to display, either a string or Markup
    :param category: The category of the message, one of "info", "warning", "error", or any custom category.
        Defaults to "info".
    :param roles: List of roles that should be shown the message. If ``None``, show to all users.
    :param html: Whether the message has safe html markup in it. Defaults to False.
    For example, show a message to all users:
    .. code-block:: python
        UIAlert("Welcome to Airflow")
    Or only for users with the User role:
    .. code-block:: python
        UIAlert("Airflow update happening next week", roles=["User"])
    You can also pass html in the message:
    .. code-block:: python
        UIAlert('Visit <a href="https://airflow.apache.org">airflow.apache.org</a>', html=True)
        # or safely escape part of the message
        # (more details: https://markupsafe.palletsprojects.com/en/2.0.x/formatting/)
        UIAlert(Markup("Welcome <em>%s</em>") % ("John & Jane Doe",))
    """
    def __init__(