The URL is correct – that signals the override. However if you do that via a simple URL ?s=rindeluit you get the same issues.
This tells me that there might be some sort of a misconfiguration on the archive page, or a custom code or another 3rd party override. The built in search from the theme should not be an issue, Flatsome uses the core WP search, which is perfectly fine.
Also, can you please make sure that nothing is selected on this panel: https://i.imgur.com/AGSwtPB.png
That may explain this as well, but it’s super rare. My best guess is still that the results page uses some sort of an archive which can’t display the results and simply skips, and therefore the 2nd page appears to be functional, as it contains the expected post types.
