Elementor Pro is required, as unfortunately the free version does not contain the Posts widget.
Easy to use
There is no "No results" text available for these widgets currently in Elementor. You can join the request thread here
Images only show up if the items have featured images
Has a working pagination
Under the Pages submenu, create a new page for this, which is going to be used as the host for the elementor widgets - and will act as the results page.
After creating the new page, open it with Elementor, and open your site admin panel on a new browser tab for convenience.
If you don't have a search bar yet, make sure to create one, you can check the basics under the Getting Started section.
Before starting a small text is needed - open up the search instance options, and click on the "Toggle Shortcodes for ..." text.
...then copy or take note of the "Elementor Posts Widget Live Filter" input text, we will need that in a moment..
Now, go back to your Elementor editor and simply put the "Posts" or the "Products" widget to a page of your choice.
Open up the Posts Widget options, and navigate to the Advanced Options panel. Enter the code that was copied/noted from step 1. It should look like this:
Save the page, and that is it.
On your WordPress back-end open up the search instance options, and navigate to the General Options -> Logic & Behavior panel.
Scroll down until you find them Magnifier and Return button events. Then set both to "Elementor results page".
Then under the "Select a page with an Elementor Pro posts widget" option, search for the previously configured page, and select it.
After the selection, the configuration should look like this.
Save the search options, and it is ready for use. Placing the search shortcode to any page will automatically redirect to the results page.
After redirection, if the plugin shortcode is present on the results page, the alternative search triggers are automatically activated - these override some redirection/live search behaviours.
These override triggers can be configured on the same options panel, General Options -> Logic & Behavior
Please read each option hint for its exact purpose.