The proble is, that the search can not produce duplicate results at all, it is not possible. The query has a distinctive directive on the Post IDs, so there is no way for the databse to output the same item twice.
If you try the live search on the back-end, you can see that there are no duplicates, and these same results are “pushed” for Elementor to display. For example this filter agains the back-end.
I feel like this might be some sort of a conflict within Elementor somewhere, something gets mixed up, but I can’t see why. My guess is, that maybe the custom template has something in relation with the problem.
Can you please try what happens, if you put this into an Elementor page, which does not use a custom template?
Also, can you please add temporary FTP access? I would love to debug the query itself, to see what exactly is going on.