If you are trying to show the vendors information that is only meant for the admin, then this will not show.
Is this related to this post? https://www.wcvendors.com/help/topic/add-shipping-class-to-order-details-in-vendor-dashboard/
If so, then you are trying to show vendors info that only the admin will be able to see.
Unless you use the Vendor Shipping, other shipping methods will only be visible or controlled by the site admin.
All other shipping methods are designed to work on a single-user WooCommerce shop. That is why we had to make the special Vendor Shipping module for WC Vendors Pro.
The vendors will only be able to see the Vendor Shipping rates within their emails or dashboards.