Streamlit session state deleted when switch page

Using Streamlit
,
3

@Charly_Wargnier Thank you) Unfortunately, i can’t share link, it is for internal using without external access. But i can share code.
start.py:

import streamlit as st
import streamlit_authenticator as stauth
import yaml
from yaml.loader import SafeLoader


def main():
    st.set_page_config(layout="wide")

    with open('config_aut.yaml', encoding="UTF-8") as file:
        config = yaml.load(file, Loader=SafeLoader)

    authenticator = stauth.Authenticate(
        config['credentials'],
        config['cookie']['name'],
        config['cookie']['key'],
        config['cookie']['expiry_days'],
        config['preauthorized']
    )

    name, authentication_status, username = authenticator.login()
    #print(name, authentication_status, username)
    #st.write(name, authentication_status, username)
    # Initialize the authentication_status key in session state
    if "authentication_status" not in st.session_state:
        st.session_state["authentication_status"] = authentication_status

    if st.session_state["authentication_status"]:
        authenticator.logout()
        st.title(f'Welcome, *{st.session_state["name"]}*')
    elif st.session_state["authentication_status"] is False:
        st.error('Username/password is incorrect')
    elif st.session_state["authentication_status"] is None:
        st.warning('Please enter your username and password')

if __name__ == "__main__":
    main()

first_page.py:

import streamlit as st

st.write(st.session_state)  
if st.session_state["authentication_status"]:
....
elif st.session_state["authentication_status"] is None:
    st.error('You must be logged in')