The results are there but hidden? If so, does the elementor grid element have the option to enable Masonry (not an issue if it does not)? The Text block that has the form in should look something like this:

[searchandfilter id="246086"]
[searchandfilter id="246086" action="filter_next_query"]
<script>(function ( $ ) {
	"use strict";
	
	// detects when the ajax request has finished and the content has been updated
	// re-init the layout scripts from Elementor
	$(document).on("sf:ajaxfinish", ".searchandfilter", function(){
		elementorFrontend.hooks.doAction('frontend/element_ready/posts.classic', jQuery('.elementor-widget-posts'));
	});
	
}(jQuery));</script>

In that order.

Elementor Anywhere is not something we have specifically tested with, and at this time we do not support it. The two most likely Display Results methods to try with it are ‘As an Archive’ (which you have tried) and Custom. With Custom, you need to place a shortcode like this:

[searchandfilter id="123456" action="filter_next_query"]

Immediately before the results loop. It may, or may not, work. I have not tested it.

Both may have problems with using Ajax, but I cannot say.