Hi,
I’m afraid results separation this way is not possible to do. It’s not because of the search plugin, but generally this is not possible only by using different kinds of widgets, because all of them will simply use the same query output. Elementor will not separate them, all of them will simply output the same thing. Even if it worked, their pagination would be broken, as potentially non-existing pages of results could appear.
Unless you are a very experienced programmer, I would not recommend doing this. In the past 12 years I have only seend 2 or 3 cases where they were able to build a custom grouped results page, and all of them were custom coded from top to bottom, as this is not possible simply via page builders.
Usually I suggest a custom code where I can, but this is far far more complicated than that, and it is not because of the search plugin either.
I recommend using either of those widgets – the posts widget works the best all around for all types of content. Another, perhaps even better possibility is to have multiple search bars for multiple types of a results and multiple results pages.
I wish this was possible, I know a few of my customers who would love this separated results page.