Dual numbers don't have efficiency concerns in a language like Julia where the dispatching occurs at compile time, so basically you get the same compiled code as you'd want from source-to-source transformations. The issue though is that all functions have to be generic. Dual numbers is a very easy form to allow the user to add their own overloads though and take advantage of how the AD works: this is much harder with source-to-source since you'd have to actually modify the AST transform. So there's a trade-off here in what is flexible.

But yes, dual numbers only do forward mode. However, slightly related is tracker types, like ReverseDiff.jl or Flux.jl's Tracker, where you essentially push a type forward through the code similarly to a dual number, and use this to build the computational graph which you then run backwards with the chain rule.