We have pro version of https://wordpress.org/plugins/admin-and-client-message-after-order-for-woocommerce/
and on the orders list in the admin panel in column “WooConvo Msgs” we don’t see notification or icon when a new message is coming from a customer.
On setting page WooConvo we have
Set the order status when the Message area is should display on user order page set Visibility on Any One, but it doesn’t work.
Please contact me so I can give you admin login to check.