Oops, it seems that an answer for the same issue was already provided 6 years ago in this forum. Posting it here to increase visibility:
The following snippet in the functions.php will fix the product title not being translated
add_filter('woocommerce_product_get_name', function($name, $product) {
$post = get_post($product->get_id());
if ($post) {
return apply_filters('sublanguage_translate_post_field', $name, $post, 'post_title');
}
return $name;
}, 10, 2);
To translate the short description, the following should be added:
add_filter('woocommerce_product_get_short_description', function($name, $product) {
$post = get_post($product->get_id());
if ($post) {
return apply_filters('sublanguage_translate_post_field', $name, $post, 'post_excerpt');
}
return $name;
}, 10, 2);