Python Requests with stream=True not working as supposed when using pipe mechanic. Trying to get distant video duration

I am trying to know the duration of a distant video file (say mp4).

I know already how to get the duration of a local video file:

import xml.etree.ElementTree as eltt, subprocess as spr

def size_from_fn(file_name):
    size = eltt.fromstring(
        spr.run(["ffprobe",
            "-i", file_name,
            "-show_format", "-output_format", "xml"
            ], stdout = spr.PIPE, stderr = spr.STDOUT).stdout.decode()
        ).find("format").get("duration")
    return size

def size_from_fd(file_descriptor):
    size = eltt.fromstring(
        spr.run(["ffprobe",
            "-i", "pipe:0",
            "-show_format", "-output_format", "xml"
            ], stdin = file_descriptor, stdout = spr.PIPE, stderr = spr.STDOUT).stdout.decode()
        ).find("format").get("duration")
    return size

def size_from_data(file_name):
    size = eltt.fromstring(
        spr.run(["ffprobe",
            "-i", "pipe:0",
            "-show_format", "-output_format", "xml"
            ], input = data, stdout = spr.PIPE, stderr = spr.STDOUT).stdout.decode()
        ).find("format").get("duration")
    return size

All work perfectly

Also I know how to get an HTTP request as a file descriptor:

import requests as rq

def url_to_fd(url):
    req = rq.get(url, stream = True)
    return req.raw

It also works

However the combination of the two fails with the message from ffprobe : Invalid data found when processing input

I have no idea why, I just know the returned file descriptor from URL has the difference of not being seekable (one-way reading) but by replacing this method of a normal file descriptor:

with open("test.mp4", "rb") as f:
    f.seek = None
    size_of_fd(f)

this works and thus shows that ffprobe doesn't use any seeking

Also doing this works so I don't know what is up:

def get_duration(url):
    complete_data = url_to_fd(url).read()
    return size_of_data(complete_data)

My problem is that video files may be arbitrarily large so I can't afford to download the whole video.

Test video URL