Again, searching and displaying a minor subset of 25k items is very different from displaying 25k items at once.
What you are looking for is to display a number of elements at once, per page, and possibly refresh that page, when the user hits the pagination. The plugins live results container is not built for this, it is to display thousands of items at once obviously, browsers will have a hard time with that.
I can think of two possibilites:
1. To increase the iteration count to display more results at once within the live container. By default this number is 10, the custom code below increases it to 100. Try adding this custom code to the functions.php in your theme/child theme directory. Before editing, please make sure to have a full site back-up just in case!
add_filter( 'asp_query_args', 'asp_change_remaining_limit_mod', 10, 2 );
function asp_change_remaining_limit_mod( $args, $id ) {
$args['_remaining_limit_mod'] = 100;
return $args;
}2. Instead of the default live results container, use an Elementor posts widget. This is a fairly new feature, but it works almost exactly as you need it. The pagination will refresh the page every time.