The first thing you need to know is the function that will initialize Masonry on your site, and whether it is available on the search results page. If you gave me a URL, I could find that for you in a few seconds. Then you would need to add a script to your site. For example, if the function were hb_masonry() then this might be the script:

(function ( $ ) {
  "use strict";
  $(document).on("sf:ajaxfinish", ".searchandfilter", function(){
    console.log("S&F JS ajax request finished");
    hb_masonry();
  });
}(jQuery));

I use the Firefox Web Developer tools and inspect the javascript. (Information -> View Javascript) and then search for masonry(

You had already put this:

(function ( $ ) {
  "use strict";
  $(document).on("sf:ajaxfinish", ".searchandfilter", function(){
    console.log("S&F JS ajax request finished");
    // ** here you need to reload your masonry script **
      
      jQuery(window).load(function() {
        
      // MASSONRY Without jquery
      var container = document.querySelector('#masonry-container');
      var msnry = new Masonry( container, {
        itemSelector: '.search-results-card',
        columnWidth: '.search-results-card',                
      });  
      
        });
  });
}(jQuery));

And I think it needs to be this:

(function ( $ ) {
  "use strict";
  $(document).on("sf:ajaxfinish", ".searchandfilter", function(){
    console.log("S&F JS ajax request finished");
    var container = document.querySelector('#masonry-container');
    var msnry = new Masonry( container, {
      itemSelector: '.search-results-card',
      columnWidth: '.search-results-card',                
    });  
  });
}(jQuery));

Maybe.

My guess is that it also needs to do more than what I see there. You may need to ask the theme author, “How do I trigger Masonry after an ajax refresh of the loop container?”

Where are you based in the world Lou? If you are in America, you will need to try to contact me early in the morning your time. I have you as a contact, and I try to show that I am online as much as I can (like now for example).