How to show specific shipping method only for certain shipping class?

in our shop we use wp-blocks scheme for the cart and checkout page.

What I would like to achieve is:

1. Show specific shipping method only for certain shipping class (or group of products) and hide other methods.
2. Show specific payment method only for certain product ids and/or certain product categories. (This is an extra question, I guess if I get how to achieve the first one, this one will be similar)

I tried to achieve it using JQuery, in custom theme script, but it seems like JQuery scripts are not applied to wp-blocks.

I used this php method to get info if the products from the cart are only from ‘my-custom-shipping-class’ shipping class.
If the answer is true, then I would like to show only one specific shipping (let’s say ‘shipping-method-1’) method and hide others.
If the answer is false, I would like to show all the mothods, except the ‘shipping-method-1’.

function show_shipping_method() {
    $slug = 'my-custom-shipping-class';
    global $woocommerce;
    $product_in_cart = false;
    $other_product_in_cart = false;
    foreach ($woocommerce->cart->get_cart() as $cart_item_key => $values) {
        $_product = $values['data'];
        $terms    = get_the_terms($_product->id, 'product_shipping_class');
        if ($terms) {
            foreach ($terms as $term) {
                $_shippingclass = $term->slug;
                if ($slug === $_shippingclass) {
                    $product_in_cart = true;
                } else {
                    $other_product_in_cart = true;
                }
            }
        } else {
            $other_product_in_cart = true;
        }
    }
    return ($product_in_cart && !$other_product_in_cart);
    
}

Then in theme html I’d add custom class:

<section id="service-page" class="<?php echo apply_filters( 'shipping_class_to_add') ? 'hide-all-shipping-except-my-custom-shipping-class' : 'hide-my-custom-shipping-class';
                                  ?>">

Then in CSS:

.hide-all-shipping-except-my-custom-shipping-class label[for="radio-control-0-flat_rate:5"],
.hide-all-shipping-except-my-custom-shipping-class label[for="radio-control-0-flat_rate:4"],
.hide-all-shipping-except-my-custom-shipping-class label[for="radio-control-0-flat_rate:1"]{
    display:none;
} 

.hide-my-custom-shipping-class label[for="radio-control-0-flat_rate:11"] {
    display: none;
}

An then, finally, JQuery code, to check the radio button of the desired shipping method (this part doesn’t work):

jQuery('document').ready(function() {
// escaping the colon doesn't change anything, none of the JQuery code works with wp-blocks
    $('input[id="radio-control-0-flat_rate:11"]').prop('checked', true);
});

Thank you in advance for help.