How to always show the stock status in WooCommerce products

In a simple product, the stock status is only displayed when you change it to anything that is not 'In stock'. Is it possible to always display the stock status?

I tried using this code:

add_filter( 'woocommerce_get_availability', 'custom_override_get_availability', 10, 2);

// The hook in function $availability is passed via the filter!
function custom_override_get_availability( $availability, $_product ) {
    if ( $_product->is_in_stock() ) $availability['availability'] = __('In Stock', 'woocommerce');
    return $availability;
}

But this overwrites my custom stock status text for some reason.

To always show the stock status in WooCommerce, without overwriting your custom status use the following:

add_filter( 'woocommerce_get_availability', 'filter_product_get_availability', 10, 2);
function filter_product_get_availability( $availability, $product ) {
    if ( $product->get_stock_status() === 'instock' ) {
        $availability['availability'] = wc_format_stock_for_display( $product );
    } elseif ( $product->managing_stock() && $product->is_on_backorder( 1 ) 
    && ! $product->backorders_require_notification() ) {
        $availability['availability'] = __('In Stock', 'woocommerce');
        $availability['class'] = 'in-stock';
    }
    return $availability;
}

Code goes in functions.php file of your child theme (or in a plugin). It should work without making trouble with your custom status.

Explanations:

The product conditional method is_in_stock() used in your IF statement is like using:

if ( 'outofstock' !== $product->get_stock_status() ) { 

So it doesn't handle other product stock statuses, especially custom ones.

See it in the source code for WC_Product is_in_stock() method.