Hi, I studied this question in more detail. The problem is in your theme. I posed other themes and this did not happen. The problem is that when I select a filter it updates the products but not the filter itself, the one that was selected is put in place of all filters and displays correct after page reload.
I’m not sure I’m seeing the issue. When I select one of the filters in the left sidebar, it filters correctly and updates the list of filters. If I then refresh, I see the same list of filters in the sidebar.
If that’s not it, any chance you could create a quick video/screenshot of the issue so I know what to look at?