### 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)

import itertools
import json
import logging
import math
import re
import sys
import traceback
import warnings
from bisect import insort_left
from collections import defaultdict
from functools import wraps
from json import JSONDecodeError
from typing import Any, Callable, Collection, Iterator, Mapping, MutableMapping, Sequence
from urllib.parse import unquote, urljoin, urlsplit
import configupdater
import flask.json
import lazy_object_proxy
import markupsafe
import nvd3
import sqlalchemy as sqla
from croniter import croniter
from flask import (
    Response,
    abort,
    before_render_template,
    flash,
    g,
    has_request_context,
    make_response,
    redirect,