Hi,
Well, the only option I see to achieve this is to completely custom code the results page.
The search plugin has no effect on how the results page looks or behaves, that is controlled by the theme (or page builder). The main issue here is that the results page is a single query, and the results are handled in a way that only items from a specific offset to a specific limit are returned for each page. This makes is nearly impossible to make groups, without doing additional queries to make grouping possible.
I have only seen one case in my career in WordPress where someone made something similar to this work (grouoping by post type on the results page), and it was very difficult. Unless you are an expert in theme coding, I wouldn’t recommend trying to achieve this – it is definitely impossible without coding.
I would love to recommend anything, but in this case there is nothing to start off as it’s only doable with custom coding. You can try contacting wpkraken for a quote about this, they may have done something similar before.