When the note list is hidden and a search is executed, a note containing the first result is opened, but it isn’t clear when that is just one of many search “hits.” The note list is filtered to the result set, but not visible unless and until the user explicitly opens it.
Since the note list is effectively the result set from a search, I think it should be shown when the search is executed. Ideally, if it was hidden when the search was executed, it should be re-hidden when the search bar is cleared.