No, Uber is not a marketplace. Uber is a consumer product. Uber designs the product and sets prices. Driver's can't compete with each other and I can't 'shop around' on Uber to find a different deal.
If Uber switches to (self driving) cars that Uber owns itself, how does that change the sales tax model? The product is still essentially the same, the consumer still pays Uber, tax shouldn't change here. The backend shouldn't dictate whether sales tax is applicable here.
Etsy is a general marketplace and should handle sales tax/GST just like Amazon does. Which it does.