entire JS folder not loading in a WP theme

The problem is die(). You can’t die() inside a template or it will stop the entire site loading at that point. If you looked closer you’d notice that it wasn’t just the JS folder that wasn’t loading, it was the whole footer.

You need to separate you code into 2 functions. One that outputs the HTML you want to output, and a second function that runs the first function and then dies.

So have the first function:

function misha_filter_function() {
    // Query posts, output loop, etc. etc.
}

Then a 2nd function, just for AJAX, that calls the first function then die():

function misha_filter_function_ajax() {
    misha_filter_function();
    die();
}

Then hook the second function for AJAX:

add_action( 'wp_ajax_myfilter', 'misha_filter_function_ajax' );
add_action( 'wp_ajax_nopriv_myfilter', 'misha_filter_function_ajax' );

The first function could also just be a template. Then in the AJAX function and template you could just use get_template_part():

function misha_filter_function_ajax() {
    get_template_part( 'partials/filter' ); // theme-directory/partials/filter.php
    die();
}

Also, you should be using GET and $_GET for this use-case. POST should be used for sending data to a server to be processed, and usually involves updating or creating a resource. GET should be used for retrieving (getting) data. You’re simply retrieving HTML, so should use the GET method.