That is correct the pricing that you see is for CPU and RAM along with OS license, the cost for the Managed disk needs to be added separately whether you go for Premium , Standard SSD or standard HDD
The only thing thats included in the price is the temp disk which is used by the OS for the paging operation and it depends on the size of the VM d4s_v3 will have a smaller size of temp db than a d16sv_3 . the cost of the temp Drive is included in the price of the VM
You are also correct by default it gives you an OS disk of 128 GB