CPT Search Form with Taxonomy filter & Or

I think you can do it in two following steps:

1. In HTML code just add a dropdown with the values you need.

   <select name="yourselect"><option value="1">Value 1</option>
   
   ...
   
   </select>
   

2. In your pre_get_posts filter add tax_query parameter like this

   if( !empty( $_GET['yourselect'] ) ) {
       $query->set('tax_query', array(
           array(
               'taxonomy' => 'YOUR_TAXONOMY_NAME',
               'field' => 'id', // or slug if you want
               'terms' => $_POST['yourselect']
           )
       );
   }
   

I’m not sure if it is a good idea to configure this way the default WordPress search. A couple months ago I already implemented similar functionality using AJAX filters. Example is here, hope it helps https://rudrastyh.com/wordpress/ajax-post-filters.html