Hello Maciej,
When you mention ‘new classes of orders’, are these order statuses? Our plugin doesn’t act upon order statuses changes but it merely attaches to order status emails. While that’s mostly the same for the default emails (each status except pending has its own transactional email), I don’t know about WooCommerce Deposits.
Checking the documentation on WooCommerce.com it confirms there is no separate email:
Deposits uses the standard WooCommerce “Customer invoice / Order details” email
https://docs.woocommerce.com/document/woocommerce-deposits/#section-20
This means that if you attach the invoice to this email it will also be included in the deposits emails. Can you confirm this?