Hi,
I thought the issue was resolved, I think I am missunderstanding something.
From what I understand, the problem was, that the plugin was not replacing the default theme search bar with the one that is created within the plugin back-end? But when I checked, the plugin search bar was visible everywhere (and it is now as well).
I guess then the problem is something else. Do you mean, that you want to keep using the default theme search bar, but have the results from this plugin? Because that is not possible unfortunately, as the plugin scripts will only work with the plugin search bar.
Let me know!