Provide a filter to add custom buttons to trigger actions by REST api. I am a developer and developed custom extensions for woocommerce. Like product price and stock synchronization with dropshippers. On admin interface I have buttons like "Synchronize this product", "Forward the order to the vendor with provided adress".
Currently we have buttons like "Begin Fulfillment", "Issue Refund", "Show Billing", "Add Note" for an order and "View product on store" for a product. Also Price, Inventory, Add shipping buttons to go to edit options for those.
I believe you can add a custom panel or buttons filter on both order and product pages. A developer can add custom panes and data to fill those panes with woocommerce filters like "woocommerceproducttabs".
This would give great flexibility to 3rd party developers to add custom data on both pages without waiting woocommerce developers.