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.
The button is not the appropriate widget to use for the desired interaction. If you want opened/closed, selected/not selected, or any kind of toggle state to be preserved between Streamlit’s re-runs, then the checkbox should be used.