I created a few test draft orders and the taxes are not being automatically included. I checked the box that states "I want to specify taxes automatically." I've added my state of Missouri for my physical presence. I've checked the box on the Products page that states "Charge taxes on this product"
Missouri is an origin-based sales tax state. Where I live, the MO state and city rate combined is 8.679%.
I'm not sure what other steps I need to do in order for the taxes to be included in the total.
Just in case you missed it I followed up on this topic here: https://ecommerce.shopify.com/c/payments-shipping-fulfilment/t/shipping-rates-by-weight-not-showing-...
It might be one of those two options, either the product doesn't have taxes applied to it or you're using an out of state address. Hope this helps :)