how to make a WordPress plugin that alters the http status of 404 pages to 200 and uses the current theme to display 404 pages output

I am working on a plugin that changes the response for 404 pages so it issues HTTP status 200 instead of 404.

I already have the status change working using code like this:

function HTTP404Template()
{
    return __DIR__.'/404_template.php';
}
    
add_filter( '404_template', 'HTTP404Template');

Then the 404_template.php has code like this:

<?php
    status_header('200');
    add_filter( 'wp_robots', 'wp_robots_no_robots' );
    get_header();
    get_footer();
?>

Although this works, it shows the current theme template defined by another plugin, but it does not show the 404 page of that theme?

How can I change the output of a 404 to make the HTTP status be 200 and still show the current theme 404 page?