Cool. I am not an expert, but I think that the issue here is the button “Try”.
When you change an entry in the multiselect box the app re-runs (this is expected behaviour).
However, when the app re-runs the button “try” returns to the “unpressed” state. It does not remember that you pushed the button.
I think the solution is the “Session_state”:
https://discuss.streamlit.io/t/multi-page-app-with-session-state/3074
https://discuss.streamlit.io/t/preserving-state-across-sidebar-pages/107
https://discuss.streamlit.io/t/when-is-the-official-session-state-support-due-for-release/10429