Way to set the NAT type?

It’d be nice to be able to change the masquerade NAT rule to be one of the many kinds of NAT available: full cone, port/address restricted cone, or symmetric. Is this possible?

No. But you can write individual srcnat rules that can do almost anything you would want.

What is the advantage of being able to set different types of NAT.
I have not run across the need for such dexterity?

Also can you give an example of how sourcenat accomplishes the same thing as cone nat or restricted etc… (given a practical example by the OP for example).

Sometimes you need to do something very specific that requires a special feature, and it’s also a selling point compared to other network OSes like IOS.

If I understand things correctly (and very likely I don’t), these terms really apply fully when one has multiple public addresses. In that case there are ways to acomplish target manually or semi-automatically under ROS.
If one only has single public address (usual situation for home users), then these terms are simply buzzwords without any meaning.

Not directly, but you can create srcnat rules that will do the same althought im not sure to understand the question correctly.