Add to cart is not hidden for the first product

Hi,
My website’s expected behavior is to hide add_to_cart button if the user isn’t logged in. However, the first product on the archive page still has the button. Here’s the code:

add_action('after_setup_theme','activate_filter') ;
 
function activate_filter(){
add_filter('woocommerce_get_price_html', 'bbloomer_show_price_logged');
}
 
function bbloomer_show_price_logged(){
	if(!is_user_logged_in() ){
		remove_action( 'woocommerce_after_shop_loop_item', 'woocommerce_template_loop_add_to_cart' );
		remove_action( 'woocommerce_single_product_summary', 'woocommerce_template_single_price', 10 );
		remove_action( 'woocommerce_single_product_summary', 'woocommerce_template_single_add_to_cart', 30 );
		remove_action( 'woocommerce_after_shop_loop_item_title', 'woocommerce_template_loop_price', 10 );
	}
}

website: http://www.viva-viva.ru

Please help! Also, is there a way not to open a cart sidebar when add_to_cart is clicked?

Thank you