It seems like this may be a limitation of st_bridge Streamlit-bridge seems unresponsive in Streamlit cloud · Issue #7 · binh-vu/streamlit-bridge · GitHub
Have you tried using st.page_link (https://docs.streamlit.io/develop/api-reference/widgets/st.page_link) in the sidebar instead of custom html? Here’s an example of what you can do, and st.page_link now supports material icons for the page icon.
Here’s a simple example of how you can use it to set up your navigation want to configure my Streamlit application so that it starts with a specific page - #2 by blackary