what can you see if you try to edit pasrsys.
Can you check if you have added initi.jsp in headlibs
<!--/* Initializes the Experience Manager authoring UI */-->
<sly data-sly-include="/libs/wcm/core/components/init/init.jsp" data-sly-unwrap/>
No Adding init.jsp also not helping ....still parsys is unclickable
I found below thread with the same issue bt this doesnt have correct answer it seems
AEM 6.3 - not add component to parsys