Still cannot prevent requests library from encoding

I have the same problem as https://github.com/psf/requests/issues/5964, but the solution does not work for me.
I need to send unescaped URL requestes to a server. The purpose is to evoke response code 400 to test the firewall configuration.

Expected Result

The following code should (according to https://github.com/psf/requests/issues/5964) send the unescaped URL:

import requests
s = requests.Session()

# Using Burp Suite Proxy to examine request being sent.
s.proxies = { 
    "http"  : "http://127.0.0.1:8080",
    "https" : "http://127.0.0.1:8080",
}
# Do not verify certificate.
s.verify = False

# Solution from https://github.com/psf/requests/issues/5964
base_url = 'https://www.example.com/search'
query = '?date_range=2017-01-01|2017-03-01'
req = requests.Request('GET', base_url)
p = req.prepare()
p.url += query
resp = s.send(p)
print(resp.request.url)

Actual Result

The print(resp.request.url) prints https://www.example.com/search?date_range=2017-01-01|2017-03-01 as expected.
But what is really transmitted is the escaped URL, https://www.example.com/search?date_range=2017-01-01%7C2017-03-01 as seen in this Burp Suite screenshot:

Reproduction Steps

Use the python code above and a way of choice to capture the actual response being sent (e.g. Burp Suite proxy).
You can also use curl to send an actually unescaped response:

curl "https://www.example.com/search?date_range=2017-01-01|2017-03-01" -x 127.0.0.1:8080 --insecure

System Information

$ python -m requests.help

{
  {
  "chardet": {
    "version": "3.0.4"
  },
  "charset_normalizer": {
    "version": "2.0.12"
  },
  "cryptography": {
    "version": ""
  },
  "idna": {
    "version": "2.8"
  },
  "implementation": {
    "name": "CPython",
    "version": "3.8.10"
  },
  "platform": {
    "release": "5.14.0-1034-oem",
    "system": "Linux"
  },
  "pyOpenSSL": {
    "openssl_version": "",
    "version": null
  },
  "requests": {
    "version": "2.27.1"
  },
  "system_ssl": {
    "version": "1010106f"
  },
  "urllib3": {
    "version": "1.25.8"
  },
  "using_charset_normalizer": false,
  "using_pyopenssl": false
}

Run the provided Python reproduction through Burp Suite and compare the prepared URL with the bytes transmitted on the wire, then inspect the request path through Requests and its urllib3 dependency. Done means determining whether the literal pipe can be transmitted without encoding while preserving normal request behavior, with a regression test covering the observed case.