I think I understand. You wish to use the Shortcode method, but create you own template. You still need to use our results.php template file, but customize it according to these instructions:
https://searchandfilter.com/documentation/search-results/using-a-shortcode/#customising-the-results
This is only a simple exemplar template, which uses the WordPress Codex structure and PHP.
So, what to do? You can replace almost anything you want in the file, but keep the if ... else ... endif
and the while .... endwhile
and transplant your own HTML, PHP and class names to replace our code. Do this slowly and test regularly, keeping backups at each stage.
The results.php template code will run inside your theme’s standard page template, in the content part, called by our results shortcode.