Hi,
Thank you for the details!
So, I think the issue is, that the page there is not actually the search results page, and redirecting to the archive will not override the items there – because overriding archive pages with the results is not possible.
However, I believe you have multiple options here to resolve:
1. Instead of using an archive, create a results page template: https://i.imgur.com/oNLBWGP.png
Make sure to remove that archive template, so the theme resolves the URL correctly, before creating a search results template.
2. Creating an actual WordPress page for the results, to which the plugin redirects to. Here you can find a tutorial for it.