Its because you check for the session state before the button, this should work
import streamlit as st
if "page" not in st.session_state:
st.session_state["page"] = 1
st.title("Test")
empty = st.empty()
if st.button("Next"):
st.session_state["page"] = 2
if st.button("Previous"):
st.session_state["page"] = 1
if st.session_state["page"] == 1:
empty.write("Page 1")
elif st.session_state["page"] == 2:
empty.write("Page 2")
else:
empty.write("No page")
Hope it helps!