Are you able to send me a live link/URL to your search page so I can take a look?

In general, instead of using the content and structure of the HTML to be found in the exemplar results.php file, you would use that inside the exemplar results-infinite-scroll.php file, but the template file that your form is using, should still be named results.php, or be numbered the same as the form ID, all as detailed here:

https://searchandfilter.com/documentation/search-results/using-a-shortcode/#customising-the-results

DO use a child theme when you do this.

The layout does not look good after the first 6 posts. Is this what you mean? If masonry is OF, is it then OK?

The problem is then that Masonry has to be re-applied on each ‘page’ load.

How do/did you apply it when the page first loads?

Maybe add this to the page also then:

<script type="text/javascript">
  $(function(){
    $(document).on("sf:ajaxfinish", ".searchandfilter", function(){
      console.log("ajax finish");
      $('.search-filter-results').masonry({
        itemSelector: '.post',
        columnWidth: '.post',
      });
    });
  }(jQuery));
</script>

I am not overly familiar with the masonry coding. We did once figure a way to do it (our developer did), see here (I have gone back through the thread to reveal most of the posts, redacting sections where needed for privacy, anything still private has nothing important in):

https://support.searchandfilter.com/forums/topic/infinite-scroll-with-masonry