### 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)

from airflow.utils.helpers import alchemy_to_dict, exactly_one
from airflow.utils.log import secrets_masker
from airflow.utils.log.log_reader import TaskLogReader
from airflow.utils.net import get_hostname
from airflow.utils.session import NEW_SESSION, create_session, provide_session
from airflow.utils.state import DagRunState, State, TaskInstanceState
from airflow.utils.strings import to_boolean
from airflow.utils.task_group import MappedTaskGroup, TaskGroup, task_group_to_dict
from airflow.utils.timezone import td_format, utcnow
from airflow.version import version
from airflow.www import auth, utils as wwwutils
from airflow.www.decorators import action_logging, gzipped
from airflow.www.forms import (
    DagRunEditForm,
    DateTimeForm,
    DateTimeWithNumRunsForm,
    DateTimeWithNumRunsWithDagRunsForm,
    TaskInstanceEditForm,
    create_connection_form_class,
)
from airflow.www.widgets import AirflowModelListWidget, AirflowVariableShowWidget
PAGE_SIZE = conf.getint("webserver", "page_size")
FILTER_TAGS_COOKIE = "tags_filter"
FILTER_STATUS_COOKIE = "dag_status_filter"
LINECHART_X_AXIS_TICKFORMAT = (
    "function (d, i) { let xLabel;"
    "if (i === undefined) {xLabel = d3.time.format('%H:%M, %d %b %Y')(new Date(parseInt(d)));"
    "} else {xLabel = d3.time.format('%H:%M, %d %b')(new Date(parseInt(d)));} return xLabel;}"
)
def truncate_task_duration(task_duration):