Python 无法通过请求模块使用网页上的应用过滤器按钮

当我导航到This WEBPAGE并输入这个搜索地址:New York City, New York, USA时，我可以在网页上看到搜索结果.我在下面粘贴的脚本可以产生相同的结果.

然而，现在我希望使用Filter results按钮来更改选项中的一些内容，例如SERVICES中的Printing  your mailpiece、DISTANCE中的within 50 miles和SORT中的By distance，然后使用Apply Filters按钮来过滤结果，这是我不能做的.

import time
import requests

url = 'https://printerdirectory.usps.com/listing/api/vendors'
link = 'https://gis.usps.com/arcgis/rest/services/locators/EDDM_Composite/GeocodeServer/suggest'
params = {
    'text': 'New York City, New York, USA',
    'f': 'json'
}
headers = {
    'User-Agent': 'Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/120.0.0.0 Safari/537.36',
    'Accept': 'application/json, text/plain, */*',
    'Accept-Encoding': 'gzip, deflate, br',
    'Accept-Language': 'en-US,en;q=0.9',
    'Origin': 'https://printerdirectory.usps.com',
    'Referer': 'https://printerdirectory.usps.com/'
}
result_params = {
    'noCache': ''
}
result_headers = {
    'User-Agent': 'Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/120.0.0.0 Safari/537.36',
    'Accept': 'application/json, text/plain, */*',
    'Accept-Encoding': 'gzip, deflate, br',
    'Accept-Language': 'en-US,en;q=0.9',
    'Host': 'printerdirectory.usps.com',
    'Referer': 'https://printerdirectory.usps.com/listing/',
    'Location': '',
    'Key': '',
    'Type': 'key',
    'Lazyupdate': '[object Object]'
}

with requests.Session() as s:
    s.headers.update(headers)
    res = s.get(link,params=params)
    result_headers['Location'] = res.json()['suggestions'][0]['text']
    result_headers['Key'] = res.json()['suggestions'][0]['magicKey']
    s.headers.update(result_headers)
    unixtime = int(time.time()*1000)
    result_params['noCache'] = unixtime
    resp = s.get(url,params=result_params)
    print(resp.json()['vendors'])

我怎样才能通过请求模块使用Apply Filters按钮？