As you are using Elementor Pro, and you should be using our extension for Elementor Pro, which can be installed after clicking the big blue button (you need to be logged in to see it) at the top of the guide page (to download the installation file):
https://searchandfilter.com/documentation/3rd-party/elementor/
I assume you are not using this extension, as the form is using the Custom display method (which our old implementation method used to use, along with some JavaScript which is not now required)
In the main, this works with another custom skin plugin (Ele Custom Skins), as that plugin sill uses the Posts widget, but adds extra skins that you design.
Doing the pagination from code is unlikely to work though.