### 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)

render_template,
    request,
    send_from_directory,
    session as flask_session,
    url_for,
)
from flask_appbuilder import BaseView, ModelView, expose
from flask_appbuilder.actions import action
from flask_appbuilder.models.sqla.filters import BaseFilter
from flask_appbuilder.security.decorators import has_access
from flask_appbuilder.urltools import get_order_args, get_page_args, get_page_size_args
from flask_appbuilder.widgets import FormWidget
from flask_babel import lazy_gettext
from jinja2.utils import htmlsafe_json_dumps, pformat  
from markupsafe import Markup, escape
from pendulum.datetime import DateTime
from pendulum.parsing.exceptions import ParserError
from pygments import highlight, lexers
from pygments.formatters import HtmlFormatter
from sqlalchemy import Date, and_, case, desc, func, inspect, union_all
from sqlalchemy.exc import IntegrityError
from sqlalchemy.orm import Session, joinedload
from wtforms import SelectField, validators
import airflow
from airflow import models, plugins_manager, settings
from airflow.api.common.mark_tasks import (
    set_dag_run_state_to_failed,
    set_dag_run_state_to_queued,
    set_dag_run_state_to_success,
    set_state,