Sort a WooCommerce product variations custom output by their price

Below I have a custom shortcode function based on this answer code that displays a block of product data for both Simple products and each variation of a Variable product. The output of the variation blocks seems to be ordered by the ID of the variation itself.

For example, this is a screenshot of the frontend output:

Which you can see matches the order of the variation IDs (from smallest to largest) screenshot:

What I would like is to sort the variations by their prices instead (NOT by their IDs) from lowest to highest. Any help is appreciated.

This is the current customized code that I have:

add_shortcode("price_variation_table", "fs_custom_available_variations_table");
function fs_custom_available_variations_table( $atts ) {

    global $post;

    // Attributes
    $atts = shortcode_atts(
        array(
            'id'    => $post->ID
        ),
        $atts, 'price_variation_table'
    );

    if( is_admin() ) return; // Only on front end

    $product = wc_get_product($atts['id']); // Get the WC_Product Object

    $output = '<div class="fs-product-data-wrapper">';

    // Variable products
    if( $product->is_type('variable'))
    {
        // Get available variations in the variable product
        $available_variations = $product->get_available_variations();

        if( count($available_variations) > 0 ){
            foreach( $available_variations as $variation )
                $output .= fs_format_product_data_output( $variation['variation_id'] );
        }
    }
    // Simple products
    elseif( $product->is_type('simple'))
    {
        $output .= fs_format_product_data_output( $product->get_id() );
    }
    else return; // Exit

    return $output .= '</div>'; // return always for a shortcode
}

// Utility funtion: getting and formtting product data
function fs_format_product_data_output( $the_id ){
    $empty =  __( '<em>(empty)</em>', 'woocommerce' );

    // Get an instance of the WC_Product_Variation object
    $product = wc_get_product( $the_id );

    // Only wc_get_price_to_display() respect if product is to be displayed with or without including taxes
    $price = wc_price( wc_get_price_to_display( $product, array( 'price' => $product->get_regular_price() ) ) );
  
    $sale_price = wc_get_price_to_display( $product, array( 'price' => $product->get_sale_price() ) );
    $sale_price = ! empty( $sale_price ) ? wc_price($sale_price) : $empty;
    // can use this class is there is no sale price set
    if ( ! $product->is_on_sale() ) {
        $no_sale_price = ' no-sale-price';
    }
  
    $size = $product->get_attribute( 'pa_size' );
    $size = ! empty( $size ) ? get_term_by( 'slug', $size, 'pa_size' )->name : $empty;

    $stock_qty = $product->get_stock_quantity();
    $stock_qty = ! empty( $stock_qty ) ? $stock_qty : '0';
    if ( $stock_qty <= 0 ) {
        $stock_status = 'stock-sold-out';
    }
    else {
        $stock_status = 'stock-available';
    }
    $output = '
    <ul class="'. $stock_status .'">
        <li class="fs-data-price">'.$price.' ea.</li>
        <li class="fs-data-size">Size: '.$size.'</li>
        <li class="fs-data-sale'. $no_sale_price .'">'.$sale_price.' ea. Preferred customer price</li>
        <li class="fs-data-stock">Quantity in Stock: '.$stock_qty.'</li>
        <li class="fs-data-notice">Quantities change quickly!</li>
    </ul>';

    return $output;
}

Try the following lightly changed code, where each displayed variations will be sorted by regular price (low to high):

add_shortcode("price_variation_table", "custom_available_variations_table");
function custom_available_variations_table( $atts ) {

    global $post;

    // Attributes
    $atts = shortcode_atts(
        array(
            'id'    => $post->ID
        ),
        $atts, 'price_variation_table'
    );

    if( is_admin() ) return; // Only on front end

    $product = wc_get_product($atts['id']); // Get the WC_Product Object

    $output = '<div class="fs-product-data-wrapper">';

    // Variable products
    if( $product->is_type('variable'))
    {
        // Get available variations in the variable product
        $available_variations = $product->get_available_variations();

        if( count($available_variations) > 0 ){
            $variations_ids = array();

            // First loop - set variations Ids in an array with regular prices
            foreach( $available_variations as $variation ){
               $product = wc_get_product( $variation['variation_id'] );
               $price = wc_price( wc_get_price_to_display( $product, array( 'price' => $product->get_regular_price() ) ) );
               $variations_ids[$variation['variation_id']] = $price;
            }
            // Sorting variation Ids using prices from lower to highest
            natsort($variations_ids);

            // 2nd Loop - Display formatted variation data
            foreach( array_keys($variations_ids) as $variations_id ){
               $output .= format_product_data_output( $variations_id );
            }
        }
    }
    // Simple products
    elseif( $product->is_type('simple'))
    {
        $output .= format_product_data_output( $product->get_id() );
    }
    else return; // Exit

    return $output .= '</div>'; // return always for a shortcode
}

// Utility funtion: getting and formatting product data
function format_product_data_output( $the_id ){
    $empty =  __( '<em>(empty)</em>', 'woocommerce' );

    // Get an instance of the WC_Product_Variation object
    $product = wc_get_product( $the_id );

    // Only wc_get_price_to_display() respect if product is to be displayed with or without including taxes
    $price = wc_price( wc_get_price_to_display( $product, array( 'price' => $product->get_regular_price() ) ) );
    $sale_price = wc_get_price_to_display( $product, array( 'price' => $product->get_sale_price() ) );
    $sale_price = ! empty( $sale_price ) ? wc_price($sale_price) : $empty;

    $size = $product->get_attribute( 'pa_size' );
    $size = ! empty( $size ) ? get_term_by( 'slug', $size, 'pa_size' )->name : $empty;

    $no_sale_price = ! $product->is_on_sale() ? ' no-sale-price' : '';

    $size = $product->get_attribute( 'pa_size' );
    $size = ! empty( $size ) ? get_term_by( 'slug', $size, 'pa_size' )->name : $empty;

    $stock_qty = $product->get_stock_quantity();
    $stock_qty = ! empty( $stock_qty ) ? $stock_qty : '0';
    $stock_status = $stock_qty <= 0 ? 'stock-sold-out' : 'stock-available';

    $output = '
    <ul class="'. $stock_status .'">
        <li class="fs-data-price">'.$price.' ea.</li>
        <li class="fs-data-size">Size: '.$size.'</li>
        <li class="fs-data-sale'. $no_sale_price .'">'.$sale_price.' ea. Preferred customer price</li>
        <li class="fs-data-stock">Quantity in Stock: '.$stock_qty.'</li>
        <li class="fs-data-notice">Quantities change quickly!</li>
    </ul>';

    return $output;
}

Code goes in function.php file of your active child theme (or active theme). Tested and works.