Embedding Spaces with auth for public models counter-intuitive?

I have the same of a similar problem. I have a private space like this

import gradio as gr

def greet(name):
    return "Hello " + name + "!!"

iface = gr.Interface(fn=greet, inputs="text", outputs="text")
iface.launch()

and a public space like this:

import os
import gradio as gr

read_key = os.environ.get('HF_TOKEN', None)

# the space is displayed, but does nothing
with gr.Blocks() as demo:
    # the loaded space should have the same version as the one it is loaded in
    # take from the space
    # take the provided hf_token
    gr.load("jen5000/demo_classification", hf_token=read_key, src="spaces")


# login works
def environ_auth(username, password):
    if username == os.environ["username"] and password == os.environ["password"]:
        return True
    else:
        return False
    

demo.queue(max_size=20)
demo.launch(auth=environ_auth).launch()

I launch the private space in the public space, but when I push the submit button of the launched space nothing happens. Is there something I am doing wrong?

SDK Versions are both 4.5.0

Cheers Jenny